Question

If x√y+1 + y√x+1 =0 and x is not equal to y, then dy/ dx=....... ​

Answer 1

Given x √(1+x) + y√(1+x) = 0

x √(1+x) = – y√(1+x)

Squaring both sides

x2(1+y) = y2(1+x)

x2 + x2y = y2 +xy2

x2-y2 = xy2 – x2y

x2-y2 = xy(y-x)

(x-y)(x+y) = -xy(x-y)

x+y = -xy

x = -y(1+x)

y = -x/(1+x)

Differentiate w.r.t.x

dy/dx = (-(1+x)+x)/(1+x)2

= (-1-x+x)/(1+x)2

= -1/(1+x)^2