Continuity and DifferentiabilityHard

Question

If x + y = 0, then equals -

Options

A.
B.
C.
D.none of these

Solution

x2(1 + y) = y2(1 + x)  ⇒  x2 - y2 + xy(x - y) = 0
⇒  (x - y) (x + y + xy) = 0
Now x ≠ y [does not satisfy the given equation]
∴  x + y + xy = 0 ⇒ y =
∴   

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