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. $noneofthese$

Answer 1

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

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