If √(x+y)+√(y−x)=a,then d2ydx2 equals

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Question

I f \sqrt{(x + y)} + \sqrt{(y - x)} = a, t h e n \frac{d^{2} y}{d x^{2}} e q u a l s

Options:

A . 2a

B . −2a2

C . 2a2

D . None of these

Answer: Option C
:
C
Given,

\sqrt{(x + y)} + \sqrt{(y - x)} = a . . . . . . . . . . (i)

∴ \sqrt{x + y} - \sqrt{y - x} = \frac{2 x}{a} . . . . . . . (i i)

A d d i n g E q s . (i) a n d (i i), t h e n

2 \sqrt{x + y} = a + \frac{2 x}{a}

S q u a r i n g, 4 x + 4 y = a^{2} + \frac{4 x^{2}}{a^{2}} + 4 x

∴ 4 + 4 \frac{d y}{d x} = 0 + \frac{8 x}{a^{2}} + 4

∴ 0 + 4 \frac{d^{2} y}{d x^{2}} = \frac{8}{a^{2}}

∴ \frac{d^{2} y}{d x^{2}} = \frac{2}{a^{2}}

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