Question

$ifA=\sqrt{7}-\sqrt{6}andB=\sqrt{6}-\sqrt{5,}then$

• A. $A>B$
• B. $A=B$
• C. $A<B$
• D. $A⩾B$

Answer 1

Answer: (C)

$A<B$

Given numbers are $A=\sqrt{7}-\sqrt{6}$ and $B=\sqrt{6}-\sqrt{5}$

Let $x=\sqrt{5}$ and $y=\sqrt{7}$ then by

$A.M$ and $G.M$

$\frac{x+y}{2}\le \sqrt{\frac{x^2+y^2}{2}}$

$\Rightarrow \frac{\sqrt{5}+\sqrt{7}}{2}\le \sqrt{6}$

$\Rightarrow \sqrt{5}+\sqrt{7}\le 2\sqrt{6}$

$\Rightarrow \sqrt{7}-\sqrt{6}\le \sqrt{6}-\sqrt{5}$