Question

решите !!!!!!!!!!!!!!!!!!!

Answer 1

Ответ:

$5$

Объяснение:

$\dfrac{(\sqrt{a^{2}+a\sqrt{a^{2}-b^{2}}}-\sqrt{a^{2}-a\sqrt{a^{2}-b^{2}}})^{2}}{2\sqrt{a^{3}b}}: \bigg (\sqrt{\dfrac{a}{b}}+\sqrt{\dfrac{b}{a}}-2 \bigg )=$

$=\dfrac{a^{2}+a\sqrt{a^{2}-b^{2}}-2\sqrt{(a^{2}+a\sqrt{a^{2}-b^{2}})(a^{2}-a\sqrt{a^{2}-b^{2}})}+a^{2}-a\sqrt{a^{2}-b^{2}}}{2\sqrt{a^{3}b}}:$

$: \bigg (\sqrt{\dfrac{a}{b}}+\sqrt{\dfrac{b}{a}}-2} \bigg )=\dfrac{2a^{2}-2\sqrt{a^{4}-a^{2}(a^{2}-b^{2})}}{2\sqrt{a^{3}b}}: \bigg (\sqrt{\dfrac{a}{b}}+\sqrt{\dfrac{b}{a}}-2} \bigg )=$

$=\dfrac{2a^{2}-2\sqrt{a^{4}-a^{4}+a^{2}b^{2}}}{2\sqrt{a^{3}b}}: \bigg (\sqrt{\dfrac{a}{b}}+\sqrt{\dfrac{b}{a}}-2} \bigg )=\dfrac{2a^{2}-2\sqrt{a^{2}b^{2}}}{2\sqrt{a^{3}b}}:$

$: \bigg (\sqrt{\dfrac{a}{b}}+\sqrt{\dfrac{b}{a}}-2} \bigg )=\dfrac{a^{2}-|ab|}{\sqrt{a^{3}b}}: \bigg (\sqrt{\dfrac{a}{b}}+\sqrt{\dfrac{b}{a}}-2} \bigg );$

$a=9, \ b=4: \ \dfrac{9^{2}-|9 \cdot 4|}{\sqrt{9^{3} \cdot 4}}: \bigg (\sqrt{\dfrac{9}{4}}+\sqrt{\dfrac{4}{9}}-2 \bigg )=\dfrac{81-36}{\sqrt{9^{2} \cdot 36}}: \bigg (\dfrac{3}{2}+\dfrac{2}{3}-2 \bigg )=$

$=\dfrac{45}{9 \cdot 6}: \bigg (\dfrac{9}{6}+\dfrac{4}{6}-\dfrac{12}{6} \bigg )=\dfrac{5}{6}: \dfrac{1}{6}=\dfrac{5}{6} \cdot 6=5;$

Answer 2

Объяснение:

$\\ \frac{( \sqrt{a {}^{2} + a \sqrt{a {}^{2} - b {}^{2} } } - \sqrt{a {}^{2} - a \sqrt{a {}^{2} - b {}^{2} } } {) {}^{2} } }{2 \sqrt{a {}^{3} b} } \div ( \sqrt{ \frac{a}{b} } + \sqrt{ \frac{b}{a} } - 2) \\ \\ \frac{( \sqrt{a {}^{2} + a \sqrt{a {}^{2} - b {}^{2} } } - \sqrt{a { }^{2} - a \sqrt{a {}^{2} - b {}^{2} } } ) {}^{2} }{2a \sqrt{ab} \times ( \sqrt{ \frac{a}{b} } + \sqrt{ \frac{b}{a} } - 2) } \\ \\ \frac{a {}^{2} + a \sqrt{a {}^{2} - b {}^{2} } - 2 \sqrt{(a {}^{2} + a \sqrt{a {}^{2} - b {}^{2} } ) \times (a {}^{2} - a \sqrt{a {}^{2} - b {}^{2} } )} + a {}^{2} - a \sqrt{a {}^{2} - b {}^{2} } }{2a \sqrt{ab} \times ( \frac{ \sqrt{a} }{ \sqrt{b} } + \frac{ \sqrt{b} }{ \sqrt{a} } - 2)} \\ \\ \frac{a {}^{2} - 2 \sqrt{a {}^{4} - a {}^{2} \times (a {}^{2} - b {}^{2} ) } + a {}^{2} }{2a \sqrt{ab} \times \frac{a + b - 2 \sqrt{ab} }{ \sqrt{ab} } } \\ \\ \frac{2a \times (a - b)}{2a \sqrt{ab} \times \frac{a + b - 2 \sqrt{ab} }{ \sqrt{ab} } } \\ \\ \frac{( \sqrt{a} - \sqrt{b} ) \times ( \sqrt{a} + \sqrt{b} )}{a + b - 2 \sqrt{ab} } \\ \\ \frac{ \sqrt{a} + \sqrt{b} }{ \sqrt{a} - \sqrt{b} } \\ \\ \\ a = 9 \\ b = 4 \\ \\ = = > \\ \\ \frac{ \sqrt{9} + \sqrt{4} }{ \sqrt{9} - \sqrt{4} } = \frac{3 + 2}{3 - 2} = \frac{5}{1} = 5$