Question

Найдите значение данного выражения!

Answer 1

$\displaystyle \frac{2}{a^{\frac{1}{2}}-b^{\frac{1}{2}} - \frac{2a^{\frac{1}{2}}{a-b} = \\\\\\ \displaystyle \frac{2}{\sqrt{a}-\sqrt{b}} - \frac{2\sqrt{a}}{(\sqrt{a}-\sqrt{b})(\sqrt{a}+\sqrt{b})} = \\\\\\ \displaystyle \frac{2(\sqrt{a}+\sqrt{b})-2\sqrt{a}}{(\sqrt{a}-\sqrt{b})(\sqrt{a}+\sqrt{b})} = \\\\\\ \displaystyle \frac{2\sqrt{a}+2\sqrt{b}-2\sqrt{a}}{a-b} = \frac{2\sqrt{b}}{a-b}$

При $a = 7 \; , \; b = 9$:

$\displaystyle \frac{2\sqrt{b}}{a-b} = \frac{2\sqrt{9}}{7 - 9} = \\\\\\ \displaystyle \frac{2 \cdot 3}{- 2} = \frac{6}{-2} = \boxed{-3}$