Home
Class 9
MATHS
If x^2=y^3, then prove that (x/y)^(3/2)+...

If `x^2=y^3`, then prove that `(x/y)^(3/2)+(y/x)^-(2/3)=x^(1/2)+y^(1/3)`.

Text Solution

Verified by Experts

The correct Answer is:
`x^(1/2)+y^(1/3)`
Promotional Banner

Topper's Solved these Questions

  • LAWS OF INDICES

    CALCUTTA BOOK HOUSE|Exercise EXERCISE - 6|67 Videos

  • HISTOGRAM AND FREQUENCY POLYGON

    CALCUTTA BOOK HOUSE|Exercise EXERCISE-2|16 Videos

  • LINEAR EQUATIONS

    CALCUTTA BOOK HOUSE|Exercise EXERCISE - 4.2|77 Videos

Similar Questions

Explore conceptually related problems

If x^(3)=y^(4) prove that (x/y)^(4/3)+(y/x)^(3/4)=x^(1/3)+y^(-1/4)

If x+y+z=xyz then prove that (3x-x^3)/(1-3x^2)+(3y-y^3)/(1-3y^2)+(3z-z^3)/(1-3z^2)=(3x-x^3)/(1-3x^2).(3y-y^3)/(1-3y^2).(3z-z^3)/(1-3z^2)

If sqrt(1-x^6)+sqrt(1-y^6) = a(x^3-y^3) then prove that (dy)/(dx)= x^2/y^2sqrt((1-y^6)/(1-x^6))

(2x-y)^(3)-(x+y)^(3)+(2y-x)^(3)

If (x^3+y^3) alpha(x^3-y^3) prove that (x^2+y^2) alpha(x^2-y^2) .

If y=x^(1/3)-x^(-1/3) , prove that y^(3)+3y=x-(1)/(x)

If log((x+y)/2) = 1/3{log x + logy + log(x+y)} , then prove that (x^2)/y + (y^2)/x = 5(x+y) .

If y=x+x^2+x^3+...oo where|x|<1,prove that x=y/(1+y)

If y=(x)/(sqrt(1+x^(2))) , prove that, x^(3)(dy)/(dx)=y^(3) .

If cottheta+tantheta=x and sectheta-costheta=y , prove that (x^2y)^(2/3)-(x y^2)^(2/3)=1