Канал: Math @ DS

Solve the equation (x+2)^4 +(x+1)^4 =17 I Math Olympiad China I

Solve the equation (x+2)^4 +(x+1)^4 =17 I Math Olympiad China I

Find the unknown length, I Math Olympiad, China I

Find the unknown length, I Math Olympiad, China I

Solve the equation x^2(y-1)+ y^2(x-1)=1 in integers I Math Olympiad, Poland I

Solve the equation x^2(y-1)+ y^2(x-1)=1 in integers I Math Olympiad, Poland I

Solve the equation x^4=(x-1)(y^2- 23)-1 in positive integer I Indian Math Olympiad Qualifiar, 2023 I

Solve the equation x^4=(x-1)(y^2- 23)-1 in positive integer I Indian Math Olympiad Qualifiar, 2023 I

Solve the exponential equation 2^a+2^b+2^c=148 in positive integers, I Math Olympiad I

Solve the exponential equation 2^a+2^b+2^c=148 in positive integers, I Math Olympiad I

Solve the equation
√a+√b=√2009
a, b being whole numbers
I Math Olympiad
I

Solve the equation √a+√b=√2009 a, b being whole numbers I Math Olympiad I

Solve the equation x^3 +x=10
I Math Olympiad
I

Solve the equation x^3 +x=10 I Math Olympiad I

Evaluate the integral
∫_0^(π/2) √((sin⁡x ) )/√(sin⁡x )⁡+√(cos⁡x ) dx

Evaluate the integral ∫_0^(π/2) √((sin⁡x ) )/√(sin⁡x )⁡+√(cos⁡x ) dx

solve for a function f, if f((2x-1)/(x-3 ))=x^2

solve for a function f, if f((2x-1)/(x-3 ))=x^2

Solve the equation
(x^2/(x^2+16))^2 +(x^2/(x^2-16))^2=20
I Math Olympiad
I

Solve the equation (x^2/(x^2+16))^2 +(x^2/(x^2-16))^2=20 I Math Olympiad I

Solve for integers a, b, if
a+2ab+b=8
I Math Olympiad
I

Solve for integers a, b, if a+2ab+b=8 I Math Olympiad I

Solve for x, y if (x+y)^2=x^2+y^2

Solve for x, y if (x+y)^2=x^2+y^2

Simplify
√(16/(4-√15) I Math Olympiad
I

Simplify √(16/(4-√15) I Math Olympiad I

Solve for a, b if
√a+√b=10,
√ab=10 I
Math Olympiad
I

Solve for a, b if √a+√b=10, √ab=10 I Math Olympiad I

If x^2 +1 /x^2 =√ 2, find x^2024- 1/x^2024

If x^2 +1 /x^2 =√ 2, find x^2024- 1/x^2024

Solve for a function f if f( (2x-1)/(x-3) )=x^2

Solve for a function f if f( (2x-1)/(x-3) )=x^2

Solve the equation x^3 +x=30 I Math Olympiad I

Solve the equation x^3 +x=30 I Math Olympiad I

Solve the equation
√x+√x=x

Solve the equation √x+√x=x

Solve the equation
(√3+√2)^(x^2-4 )+(√3-√2)^(x^2-4 )=10
I Math Olympiad
I I IIT JEE I

Solve the equation (√3+√2)^(x^2-4 )+(√3-√2)^(x^2-4 )=10 I Math Olympiad I I IIT JEE I

Solve the inequality 2x+1 /x-2 is greater then 1

Solve the inequality 2x+1 /x-2 is greater then 1

Find the value of square root of the sum 1+2+3+...+36

Find the value of square root of the sum 1+2+3+...+36

If x+1/x = √2 , find the value of x^777+1/x^777

If x+1/x = √2 , find the value of x^777+1/x^777

Solve for x, an equation involving radicals

Solve for x, an equation involving radicals

Solve the equation x^2 +x^2/(x+1)^2=3 I Math Olympiad I

Solve the equation x^2 +x^2/(x+1)^2=3 I Math Olympiad I

Solve the equation x^6=(x- 2)^6 I Math Olympiad I

Solve the equation x^6=(x- 2)^6 I Math Olympiad I

Which is bigger e^ pi or pi^e I Math Olympiad I I IB HL Math I

Which is bigger e^ pi or pi^e I Math Olympiad I I IB HL Math I

If (1+a)(1+b)(a+b)=2022, a^3+b^3=1933, find the value of a+b I Math Olympiad I

If (1+a)(1+b)(a+b)=2022, a^3+b^3=1933, find the value of a+b I Math Olympiad I

Solve the equation, x th root of 2 equals to 3

Solve the equation, x th root of 2 equals to 3

Solve the equation a^9+a^6=36, for a real number a

Solve the equation a^9+a^6=36, for a real number a

Simplify I Math Olympiad I

Simplify I Math Olympiad I

Which is greater 40^41 or 41^40 I Math Olympiad I

Which is greater 40^41 or 41^40 I Math Olympiad I

Which is bigger 222^333 or 333^222

Which is bigger 222^333 or 333^222

Solve the equation 8^x+50^x=20^(x+1)
I Math Olympiad
I

Solve the equation 8^x+50^x=20^(x+1) I Math Olympiad I

Solve for x, 5^(x+6)=6^x + 5, I Math Olympiad USA I

Solve for x, 5^(x+6)=6^x + 5, I Math Olympiad USA I

Solve for x, x^3-(3+√3)x+3=0 l Math Olympiad I

Solve for x, x^3-(3+√3)x+3=0 l Math Olympiad I

Solve for x,y x^2=5+y, y^2=5+x

Solve for x,y x^2=5+y, y^2=5+x

Which is bigger 1.005^200 or 2, ( without using calculator) I Math Olympiad I

Which is bigger 1.005^200 or 2, ( without using calculator) I Math Olympiad I

If sin A =k sin B, then prove that tan(A-B)/2 =(k-1)/(k+1) tan (A+B)/2

If sin A =k sin B, then prove that tan(A-B)/2 =(k-1)/(k+1) tan (A+B)/2

Solve for x, root of x times root of times root of x =2, √(x√(x√x) ) =2
x=?
I Math Olympiad
I

Solve for x, root of x times root of times root of x =2, √(x√(x√x) ) =2 x=? I Math Olympiad I

Find the value of a^2+b^2+c^2 if ab=1000, bc=2000, ca =3000 I Math Olympiad I

Find the value of a^2+b^2+c^2 if ab=1000, bc=2000, ca =3000 I Math Olympiad I

Solve the equation, 10^x+100^x=1000^x |Math Olympiad I

Solve the equation, 10^x+100^x=1000^x |Math Olympiad I

Find the value of x+y if x^2-y^2=24, xy =35 I Math Olympiad l

Find the value of x+y if x^2-y^2=24, xy =35 I Math Olympiad l

If x+1/x =√2, find x^2021+1/x^2021 I Math Olympiad I

If x+1/x =√2, find x^2021+1/x^2021 I Math Olympiad I

Solve the equation x^6=(x -1)^6 I Math Olympiad I

Solve the equation x^6=(x -1)^6 I Math Olympiad I

Solve the equation 2a^2 - 2b^2=98, in integers I Math Olympiad I

Solve the equation 2a^2 - 2b^2=98, in integers I Math Olympiad I

$Simplify {1/(99-70√2)^5 }^(1/6) | Math Olympiad |$

Simplify {1/(99-70√2)^5 }^(1/6) | Math Olympiad |

Ladder and box problem, determine the height of the ladder above the box, algebraic proof

Ladder and box problem, determine the height of the ladder above the box, algebraic proof

Solve the equation 1+2^x+2^(2x+1)=y^2 in integers | International Math Olympiad

|

Solve the equation 1+2^x+2^(2x+1)=y^2 in integers | International Math Olympiad |

Simplify
((√39+√3)/√12)^7
| Math Olympiad
|

Simplify ((√39+√3)/√12)^7 | Math Olympiad |

Solve the equation

Solve the equation

Solve the equation (xy-7)^2=x^2+y^2, for positive integers x,y, I Math Olympiad I

Solve the equation (xy-7)^2=x^2+y^2, for positive integers x,y, I Math Olympiad I

Solve the system of equation x+yz=2, y+zx=2, z+xy=2 | Math Olympiad |

Solve the system of equation x+yz=2, y+zx=2, z+xy=2 | Math Olympiad |

If ( k+1)/ k =1 then find the value of k^15 I Math olympiad I

If ( k+1)/ k =1 then find the value of k^15 I Math olympiad I

If, a+b=1, a^2+b^2 =2, find a^8+b^8

If, a+b=1, a^2+b^2 =2, find a^8+b^8

Factorize a^5 +a^4+1

Factorize a^5 +a^4+1

Solve the system of equations simultaneously, x^2+yz=1, y^2-xz=0, z^2+xy=1 | math Olympiad |

Solve the system of equations simultaneously, x^2+yz=1, y^2-xz=0, z^2+xy=1 | math Olympiad |

Solve the equation
a^2+b^2+4b=96,
in positive integers
| Warm up for Math Olympiad
|

Solve the equation a^2+b^2+4b=96, in positive integers | Warm up for Math Olympiad |

Solve for x , √(1+√(1+x)) = x^(1/3) | Math Olympiad |

Solve for x , √(1+√(1+x)) = x^(1/3) | Math Olympiad |

Solve the equation 9^x +33^x =121^x | Math Olympiad |

Solve the equation 9^x +33^x =121^x | Math Olympiad |

Solve the equation x^6 - x^2 =2 | Math Olympiad |

Solve the equation x^6 - x^2 =2 | Math Olympiad |

Solve the equation 2^x+4^x+8^x=155 | Math Olympiad |

Solve the equation 2^x+4^x+8^x=155 | Math Olympiad |

Find x+y ,if x^2+y^2 =7, x^3+y^3 =10 | Math Olympiad |

Find x+y ,if x^2+y^2 =7, x^3+y^3 =10 | Math Olympiad |

Evaluate the integral 2x(1+sin x)/(1+ cos^2 x) I IIT JEE I

Evaluate the integral 2x(1+sin x)/(1+ cos^2 x) I IIT JEE I

Solve the equation Ix+6I+Ix-1I=6, sum of modulus of x+ 6 and x-1 is equal to 6

Solve the equation Ix+6I+Ix-1I=6, sum of modulus of x+ 6 and x-1 is equal to 6

Solve the equation x^5+x^4+x^3+x^2+x^1= -1 | Math Olympiad |

Solve the equation x^5+x^4+x^3+x^2+x^1= -1 | Math Olympiad |

Solve for x, 1/x+1/m+1/n= 1/(x+m+n)

Solve for x, 1/x+1/m+1/n= 1/(x+m+n)

Solve for x, y, if x^2 -y =43, y^2 - x=43 | Math Olympiad |

Solve for x, y, if x^2 -y =43, y^2 - x=43 | Math Olympiad |

Solve for positive integers x, y, z, that satisfy the equality 4^x+4^y+4^z=192 | Math Olympiad |

Solve for positive integers x, y, z, that satisfy the equality 4^x+4^y+4^z=192 | Math Olympiad |

If x+y=10, xy=20, find 1/x + 1/y

If x+y=10, xy=20, find 1/x + 1/y

Solve for x , (4+√15)^x +(4- √15)^x=62 |Math Olympiad |

Solve for x , (4+√15)^x +(4- √15)^x=62 |Math Olympiad |

Integrate 1 by sin x + cosx +1

Integrate 1 by sin x + cosx +1

Find the value of ((1+√5)/2)^12 | Math Olympiad |

Find the value of ((1+√5)/2)^12 | Math Olympiad |

Solve for a positive integer x, 8^x +2^x =130 |Math Olympiad|

Solve for a positive integer x, 8^x +2^x =130 |Math Olympiad|

Is square root (-8 × -9 ) =(square root -8) × square root (-9) Is
√((-8)×(-9))=√(-8)×√(-9)
? in C

Is square root (-8 × -9 ) =(square root -8) × square root (-9) Is √((-8)×(-9))=√(-8)×√(-9) ? in C

Solve for a, b, if √a+√b=10, √ab=10 | math Olympiad |

Solve for a, b, if √a+√b=10, √ab=10 | math Olympiad |

Evaluate the integral of 1 by e^x+e^-x

Evaluate the integral of 1 by e^x+e^-x

Solve for the integers a,b,c, 2^a+2^b+2^c=148 | Math Olympiad |

Solve for the integers a,b,c, 2^a+2^b+2^c=148 | Math Olympiad |

Solve for the real numbers a, b, c if ab= 35, bc=56, ca = 40

Solve for the real numbers a, b, c if ab= 35, bc=56, ca = 40

Find all positive integer m such that 3^m - 2^m=65 |math Olympiad|

Find all positive integer m such that 3^m - 2^m=65 |math Olympiad|

Find the domain of the function f(x)= square root of log (x^2-6x+6) |math Olympiad|, | IIT JEE|

Find the domain of the function f(x)= square root of log (x^2-6x+6) |math Olympiad|, | IIT JEE|

Evaluate the integral of 1/(e^x+e^-x)

Evaluate the integral of 1/(e^x+e^-x)

Solve the equation x-4 =√(x-2)

Solve the equation x-4 =√(x-2)

Simplify (1+i)^18

Simplify (1+i)^18

Calculate the value of 2^18 -1, without a calculator

Calculate the value of 2^18 -1, without a calculator

Solve the differential equation dy/dx =1/(x+y)

Solve the differential equation dy/dx =1/(x+y)

Solve for x, y if x^2 =y+1, y^2=x+1, a question in math olympiad

Solve for x, y if x^2 =y+1, y^2=x+1, a question in math olympiad

Integrate x / (1+ sin x)

Integrate x / (1+ sin x)

Evaluate ∫_0^1 √(-log x) dx

Evaluate ∫_0^1 √(-log x) dx

Which is greater 50^50 or 49^51, | math olympiad |

Which is greater 50^50 or 49^51, | math olympiad |

Solve the equation x+y+xy=55, in integers x,y

Solve the equation x+y+xy=55, in integers x,y

Solve the equation square root of x =equals to -1 in the set of real numbers

Solve the equation square root of x =equals to -1 in the set of real numbers

Evaluate the line integral along a circle

Evaluate the line integral along a circle

Evaluate the integral 0 to π/2 sin^10 x dx

Evaluate the integral 0 to π/2 sin^10 x dx

Evaluate the integral 0 to π/4 log 1+ tan x

Evaluate the integral 0 to π/4 log 1+ tan x

Evaluate the integral of tan inverse x

Evaluate the integral of tan inverse x

Solve the equation a^4=(a-1)^4, a math olympiad question

Solve the equation a^4=(a-1)^4, a math olympiad question

Solve the equation x^2 - y^2 =19 in integers, a question in math olympiad

Solve the equation x^2 - y^2 =19 in integers, a question in math olympiad

Solve The Equation x^2 - x^3 =12 | math Olympiad |

Solve The Equation x^2 - x^3 =12 | math Olympiad |

Evaluate the integral ∫x cos⁡nx dx,n=1,2,3,⋯

Evaluate the integral ∫x cos⁡nx dx,n=1,2,3,⋯

Prove that vector field is conservative

Prove that vector field is conservative

Find all the integers a, b if 2^a - 2^b=2016, | math olympiad |

Find all the integers a, b if 2^a - 2^b=2016, | math olympiad |

Simplify the number √(√9-√8) that is simplify square root of ( square root 9- square root 8 )

Simplify the number √(√9-√8) that is simplify square root of ( square root 9- square root 8 )

Evaluate the integral

Evaluate the integral

Obtain a fourier cosine series for f(x)=x

Obtain a fourier cosine series for f(x)=x

Which number is greater 40^41 or 41^40 ? (Calculator not allowed), a math olympiad question

Which number is greater 40^41 or 41^40 ? (Calculator not allowed), a math olympiad question

Apply Gauss divergence theorem to evaluate the surface integral

Apply Gauss divergence theorem to evaluate the surface integral

Find square root of 1+i

Find square root of 1+i

Obtain a fourier series for f(x) =x-x^2

Obtain a fourier series for f(x) =x-x^2

Trisect a line segment using ruler and compass only

Trisect a line segment using ruler and compass only

Find the approximate value of square root of 2 by newton raphson method.

Find the approximate value of square root of 2 by newton raphson method.

Evaluate the integral of e^ax sin(bx+c)

Evaluate the integral of e^ax sin(bx+c)

Find the derivative of x sin x using first principle or definition of derivatives

Find the derivative of x sin x using first principle or definition of derivatives

Determine the radius of curvature for y^2=4x at the origin

Determine the radius of curvature for y^2=4x at the origin

If z=cos θ+ i sin θ, then find
z^n+1/z^n

If z=cos θ+ i sin θ, then find z^n+1/z^n

Solve the differential equation dy/dx=√(y-1)/(x-1)

Solve the differential equation dy/dx=√(y-1)/(x-1)

If y=x+x^/2+ x^3/3+...then express x in term y

If y=x+x^/2+ x^3/3+...then express x in term y

Show that the sum of series is square root of 2/3

Show that the sum of series is square root of 2/3

Evaluate the integral ∫(cos x-sin x)/√sin⁡2x dx

Evaluate the integral ∫(cos x-sin x)/√sin⁡2x dx

Evaluate the limit lim x →1 ln⁡(1-x)/cot πx

Evaluate the limit lim x →1 ln⁡(1-x)/cot πx

Integrate square root of a - x by x

Integrate square root of a - x by x

How to draw a square, without using a set square or a compass or a protractor?

How to draw a square, without using a set square or a compass or a protractor?

express in polar form

express in polar form

Draw a circumcircle and incircumcircle to a triangle

Draw a circumcircle and incircumcircle to a triangle

Obtain a Maclaurin's series for sin x

Obtain a Maclaurin's series for sin x

Obtain Maclaurin series for f(x)=e^x

Obtain Maclaurin series for f(x)=e^x

Evaluate the limit of x cot theta -theta cot x by x -theta as x tends to theta

Evaluate the limit of x cot theta -theta cot x by x -theta as x tends to theta

If x+1/x =root 3, find x^100+1/x^100

If x+1/x =root 3, find x^100+1/x^100

Prove that b^n -1 is a multiple of b-1 for any integer b different from 1

Prove that b^n -1 is a multiple of b-1 for any integer b different from 1

Find the value of cos 15 degrees

Find the value of cos 15 degrees

Obtain a fourier transform of a function

Obtain a fourier transform of a function

Flower of circles

Flower of circles

Prove that derivative of sin x is cos x

Prove that derivative of sin x is cos x

Find the determinant without expanding

Find the determinant without expanding

Prove that root 2 is an irrrational number

Prove that root 2 is an irrrational number

Prove the parallelogram identity using vectors

Prove the parallelogram identity using vectors

Evaluate the integral 0 to infinity e^-x^2 dx

Evaluate the integral 0 to infinity e^-x^2 dx

Apply Sieve of Eratosthenes method to identify prime numbers from 1 to 36

Apply Sieve of Eratosthenes method to identify prime numbers from 1 to 36

Find the radius of curvature, r^3=a^3 cos 3 theta

Find the radius of curvature, r^3=a^3 cos 3 theta

Find square root of i, imaginary number

Find square root of i, imaginary number

Evaluate the integral of secx (sec x + tan x) dx

Evaluate the integral of secx (sec x + tan x) dx

Obtain a fourier series for x^2

Obtain a fourier series for x^2

Evaluate the integral 1 by root of 4x - x^2

Evaluate the integral 1 by root of 4x - x^2

Evaluate the integral e^ax sin bx

Evaluate the integral e^ax sin bx

Draw a regular hexagon of side 5 cm using set square

Draw a regular hexagon of side 5 cm using set square

Determine the limit

Determine the limit

De Moivre's theorem, sixth root of 1, hexagon, unit circle

De Moivre's theorem, sixth root of 1, hexagon, unit circle

Integrate sinx/x 0 to infinity

Integrate sinx/x 0 to infinity

Evaluate the integral 0 to pi /2 log(sin x) dx

Evaluate the integral 0 to pi /2 log(sin x) dx

Solve the equation

Solve the equation

Prove by mathematical induction 2^3n -1 is divisible by 7

Prove by mathematical induction 2^3n -1 is divisible by 7

Find the radius of curvature, x=a(θ+sin⁡θ ), y=a(1-cos⁡θ )

Find the radius of curvature, x=a(θ+sin⁡θ ), y=a(1-cos⁡θ )

Find the value of Γ(1/2), Gamma(1/2)

Find the value of Γ(1/2), Gamma(1/2)

Evaluate the definite integral 0 to pi x log (sin x) dx

Evaluate the definite integral 0 to pi x log (sin x) dx

Prove that Γ(p+1) = p Γ(p)

Prove that Γ(p+1) = p Γ(p)

Root of 2 plus root of 2 plus ...

Root of 2 plus root of 2 plus ...

Draw a flower of circles

Draw a flower of circles

Evaluate the integral

Evaluate the integral

Evaluate the integral

Evaluate the integral

Rotate a trapezium to get a square

Rotate a trapezium to get a square

Find a number equal to its reciprocal, x=1/x

Find a number equal to its reciprocal, x=1/x

Factorize

Factorize

Evaluate the limit by applying L'Hospital's Rule

Evaluate the limit by applying L'Hospital's Rule

Flower of circles

Flower of circles

Draw a flower of circles and colour it

Draw a flower of circles and colour it

Determine the radius of curvature for the curve r=a cos theta

Determine the radius of curvature for the curve r=a cos theta

Solve the equation x^5= x^2

Solve the equation x^5= x^2

Draw a flower of circle

Draw a flower of circle

Evaluate the integral

Evaluate the integral

Draw a regular hexagon by semi circle method

Draw a regular hexagon by semi circle method

Evaluate the limit

Evaluate the limit

Draw a symmetric hexagram and color it

Draw a symmetric hexagram and color it

Draw three circles that just touch each other

Draw three circles that just touch each other

Reduce the differential equation to linear form and solve it

Reduce the differential equation to linear form and solve it

Draw a regular hexagon just using a strip of paper and pen

Draw a regular hexagon just using a strip of paper and pen

Draw a unicursal hexagram

Draw a unicursal hexagram

Solve the trigonometric equation

Solve the trigonometric equation

Is mod of x square same as x square

Is mod of x square same as x square

Solve the differential equation by applying variable separable method for xy (y+1) dy-(x^2+1 ) dx =0

Solve the differential equation by applying variable separable method for xy (y+1) dy-(x^2+1 ) dx =0

$Apply partial fraction to integrate$

Apply partial fraction to integrate

Find the HCF of 0 and 10

Find the HCF of 0 and 10

Find the HCF or gcd of 0 and 8

Find the HCF or gcd of 0 and 8

Different method of drawing a circle

Different method of drawing a circle

Find the HCF of 0 and 10

Find the HCF of 0 and 10

Draw a regular hexagon

Draw a regular hexagon

Draw a unicursal hexagram

Draw a unicursal hexagram

Draw a perpendicular bisector of a line segment measuring 7 cm

Draw a perpendicular bisector of a line segment measuring 7 cm

Prove by mathematical induction that n(n+1)(n+2) is divisible by 6

Prove by mathematical induction that n(n+1)(n+2) is divisible by 6

Evaluate the Limit of (|x|)/x as x approaches 0

Evaluate the Limit of (|x|)/x as x approaches 0

Is Rolle's theorem applicable for f(x)=x^2/3 on [-1,1 ] ?

Is Rolle's theorem applicable for f(x)=x^2/3 on [-1,1 ] ?

Draw a regular hexagon of side 5 cm by semicircle method

Draw a regular hexagon of side 5 cm by semicircle method

Prove by mathematical induction that n^5-n is divisible by 5

Prove by mathematical induction that n^5-n is divisible by 5

Find the limit

Find the limit

Evaluate the integral

Evaluate the integral

Evaluate the integral

Evaluate the integral

$Evaluate the integral \int x^2 /x^2-4 \:dx$

Evaluate the integral \int x^2 /x^2-4 \:dx

Evaluate the integral e^3x sin 5x

Evaluate the integral e^3x sin 5x

Prove by mathematical induction that 2^n is greater than n^2 for n greater than 4

Prove by mathematical induction that 2^n is greater than n^2 for n greater than 4

Consistent and inconsistent system of equation

Consistent and inconsistent system of equation

Draw an equilateral triangle that fits exactly outside a circle

Draw an equilateral triangle that fits exactly outside a circle

Solve the differential equation

Solve the differential equation