Question

решить б в г срочна 35 балов

Answer 1

б)

$\frac{1}{1 - \sqrt{2} } = \frac{1}{1 - \sqrt{2} } * \frac{1 + \sqrt{2}}{1 + \sqrt{2} }=\\\\= \frac{1+\sqrt{2} }{(1-\sqrt{2}) * (1+\sqrt{2})} = \frac{1+\sqrt{2} }{1 - 2} =\\\\= -1 - \sqrt{2}$

в)

$\frac{1}{\sqrt{x} -\sqrt{y} } =\frac{1}{\sqrt{x} -\sqrt{y} } *\frac{\sqrt{x} +\sqrt{y} }{\sqrt{x} +\sqrt{y} } = \frac{\sqrt{x} +\sqrt{y} }{(\sqrt{x} -\sqrt{y} )*(\sqrt{x} +\sqrt{y} ) } = \\\\= \frac{\sqrt{x} +\sqrt{y} }{x-y}$

г)

$\frac{a}{\sqrt{a}+\sqrt{b} }=\frac{a}{\sqrt{a}+\sqrt{b} }*\frac{\sqrt{a}-\sqrt{b}}{\sqrt{a}-\sqrt{b} } = \frac{a*(\sqrt{a}-\sqrt{b})}{(\sqrt{a}+\sqrt{b})*(\sqrt{a}-\sqrt{b})} =\\\\= \frac{a\sqrt{a} - a\sqrt{b} }{a-b}$