If x^2+y^2=t+ 1 t , x^4+y^4=t^2+ 1 t^2 , then x^3 y d y d x is equal to

Step-by-step solution

Given, x^4+y^4=t^2+ 1 t^2 aligned & = (t+ 1 t )^2-2 & = (x^2+y^2 )^2-2 ( x^2+y^2=t+ 1 t , given ) & x^4+y^4=x^4+y^4+2 x^2 y^2-2 & x^2 y^2=1 & y^2= 1 x^2 aligned On differentiating w.r.t. x , we get aligned & 2 y d y d x =- 2 x^3 & x^3 y d y d x =-1 aligned