Question

$If\sqrt{(x+y)}+\sqrt{(y-x)}=a,then\frac{d^{2}y}{d{x}^2}equals$

• A. $\frac{2}{a}$
• B. $\frac{-2}{a^2}$
• C. $\frac{2}{a^2}$
• D. None of these

Answer 1

The correct option is C $\frac{2}{a^2}$

Given,
$\sqrt{(x+y)}+\sqrt{(y-x)}=a..........\left(i\right)$
$\therefore \sqrt{x+y}-\sqrt{y-x}=\frac{2x}{a}.......\left(ii\right)$
$AddingEqs.\left(i\right)and\left(ii\right),then$
$2\sqrt{x+y}=a+\frac{2x}{a}$
$Squaring,4x+4y=a^2+\frac{4x^2}{a^2}+4x$
$\therefore 4+4\frac{dy}{dx}=0+\frac{8x}{a^2}+4$
$\therefore 0+4\frac{d^{2}y}{d{x}^2}=\frac{8}{a^2}$
$\therefore \frac{d^{2}y}{d{x}^2}=\frac{2}{a^2}$