Question

пожалуйста помогите я не могу уже​

Answer 1

Ответ:

$\displaystyle-\frac{29}{6} = -4\frac{5}{6}$

Объяснение:

Подставим значения m и n в уравнение.

m = 5, n= 20. Получим:

$\displaystyle \frac{5+2\sqrt{5*20} +20}{20} *\frac{\sqrt{5*20} +20 }{5-20} - \frac{\sqrt{5} }{\sqrt{5} +\sqrt{20} }$

$\displaystyle \frac{5+2*10+20 }{20} *\frac{10+20}{5-20} -\frac{\sqrt{5} }{3\sqrt{5} }$

$\displaystyle\frac{5+20+20}{20}*\frac{30}{5-20} -\frac{1}{3}$

$\displaystyle\frac{45}{20} *\frac{30}{5-20} -\frac{1}{3}$

$\displaystyle\frac{9}{4} *\frac{30}{5-20} -\frac{1}{3\\}$

$\displaystyle\frac{9}{2} *\frac{15}{5-20} -\frac{1}{3\\}$

$\displaystyle\frac{135}{2(5-20)} -\frac{1}{3}$

$\displaystyle\frac{135}{2(-15)} -\frac{1}{3}$

$\displaystyle -\frac{135}{2*15} -\frac{1}{3\\}$

$\displaystyle -\frac{9}{2}- \frac{1}{3}$

$\displaystyle -\frac{27+2}{6}$

$\displaystyle-\frac{29}{6} = -4\frac{5}{6}$

Answer 2

1)

$\frac{m + 2 \sqrt{mn} + n }{n} \times \frac{ \sqrt{mn} + n }{m - n} = \\ = \frac{( \sqrt{m} ) {}^{2} + 2 \sqrt{m} \sqrt{n} + ( \sqrt{n} ) {}^{2} }{ \sqrt{n} \sqrt{n} } \times \frac{ \sqrt{n} ( \sqrt{m} + \sqrt{n}) }{( \sqrt{m} ) {}^{2} - ( \sqrt{n}) {}^{2} } = \\ = \frac{( \sqrt{m} + \sqrt{n}) {}^{2} \times ( \sqrt{m} + \sqrt{n} ) }{ \sqrt{n}( \sqrt{m} + \sqrt{n} )( \sqrt{m} - \sqrt{n} ) } = \\ = \frac{( \sqrt{m} + \sqrt{n}) {}^{2} }{ \sqrt{n}( \sqrt{m} - \sqrt{n}) }$

2)

$\frac{( \sqrt{m} + \sqrt{n}) {}^{2} }{ \sqrt{n}( \sqrt{m} - \sqrt{n}) } - \frac{ \sqrt{m} }{ \sqrt{m} + \sqrt{n} } = \\ = \frac{( \sqrt{m} + \sqrt{n} ) {}^{3} - \sqrt{mn}( \sqrt{m} - \sqrt{n} )}{ \sqrt{n}( \sqrt{m} - \sqrt{n}) ( \sqrt{m} + \sqrt{n} } = \\ = \frac{( \sqrt{m} + \sqrt{n} ) {}^{3} - \sqrt{mn}( \sqrt{m} - \sqrt{n} )}{ \sqrt{n}( m - n) }$

3)

$m = 5 \: \: \: ( \sqrt{m} = \sqrt{5}) \\ n = 20 \: \: \: ( \sqrt{n} = 2 \sqrt{5} )\\ \frac{( \sqrt{m} + \sqrt{n} ) {}^{3} - \sqrt{mn}( \sqrt{m} - \sqrt{n} )}{ \sqrt{n}( m - n) } = \\ = \frac{( \sqrt{5} + 2 \sqrt{5}) {}^{3} - 2 \sqrt{5} \sqrt{5} ( \sqrt{5} - 2 \sqrt{5}) }{2 \sqrt{5}(5 - 20) } = \\ = \frac{(3 \sqrt{5}) {}^{3} - 10 \times ( - \sqrt{5} ) }{2 \sqrt{5} \times ( - 15) } = \\ = \frac{135 \sqrt{5} + 10 \sqrt{5} }{ - 30 \sqrt{5} } = - \frac{145 \sqrt{5} }{30 \sqrt{5} } = \\ = - \frac{145}{30} = - \frac{29}{6} = - 4 \frac{5}{6}$