If y^ 1 m +y^ -1 m =2 x, x^1 1 , then (x^2-1 ) ( d y d x )^2 is equal to

Step-by-step solution

y^ 1 m +y^ - 1 m =2 x y^ 2 m +y^ - 2 m +2=4 x^2 . . (1) aligned & 1 m (y^ 1 m -1 -y^ - 1 m -1 ) d x d y =2 & (y^ 1 m -y^ - 1 m )= 2 m y d y d x & y^ 2 m +y^ - 2 m -2= 4 m^2 y^2 ( d y d x )^2 .(2) [squaring both sides] aligned from (1)-(2) aligned & 4=4 x^2- 4 m^2 y^2 ( d y d x )^2 4 ( d y d x )^2=4 x^2 ( d y d x )^2-4 m^2 y^2 & (x^2-1 ) ( d y d x )^2=m^2 y^2 aligned