Question

If $x=\sqrt{7}-\sqrt{5}$ and $y=\sqrt{13}-\sqrt{11}$, then

• A. $x>y$
• B. $x<y$
• C. $x=y$
• D. None of these

Answer 1

The correct option is A $x>y$

$x=\sqrt{7}-\sqrt{5}=\frac{2}{\sqrt{7}+\sqrt{5}}$
$y=\sqrt{13}-\sqrt{11}=\frac{2}{\sqrt{13}+\sqrt{11}}$
$\because \sqrt{7}+\sqrt{5}<\sqrt{13}+\sqrt{11}$
$\therefore x>y$