Question

( 2 × √ $\frac{2}{5}$ - 5 × √($\frac{5}{8}$ + 4 × √ $\frac{5}{2}$ ) × √ $\frac{2}{5}$ =?



Cu rezolvare completa va rog!

Answer 1

Explicație pas cu pas:

$\bigg(2 \cdot \sqrt{ \dfrac{2}{5}} - 5 \cdot \sqrt{ \dfrac{5}{8} } + 4 \cdot \sqrt{ \dfrac{5}{2}} \bigg) \cdot \sqrt{ \dfrac{2}{5}} =$

$= \bigg( \dfrac{ 2\sqrt{2} }{ \sqrt{5} } - \dfrac{ 5\sqrt{5} }{2 \sqrt{2} } + \dfrac{4 \sqrt{5} }{ \sqrt{2} } \bigg) \cdot \dfrac{ \sqrt{2} }{ \sqrt{5} }$

$= \bigg( \dfrac{ 2\sqrt{10} }{5} - \dfrac{ 5\sqrt{10} }{4} + \dfrac{4 \sqrt{10} }{2} \bigg) \cdot \dfrac{ \sqrt{10} }{5}$

$= \bigg( \dfrac{ 8\sqrt{10} }{20} - \dfrac{ 25\sqrt{10} }{20} + \dfrac{40 \sqrt{10} }{20} \bigg) \cdot \dfrac{ \sqrt{10} }{5}$

$= \dfrac{ 8\sqrt{10} - 25\sqrt{10} + 40 \sqrt{10}}{20} \cdot \dfrac{ \sqrt{10} }{5}$

$= \dfrac{ 23 \sqrt{10}}{20} \cdot \dfrac{ \sqrt{10} }{5} = \dfrac{23 \cdot 10}{20 \cdot 5} = \bf \dfrac{23}{10}$

sau:

$\bigg(2 \cdot \sqrt{ \dfrac{2}{5}} - 5 \cdot \sqrt{ \dfrac{5}{8} } + 4 \cdot \sqrt{ \dfrac{5}{2}} \bigg) \cdot \sqrt{ \dfrac{2}{5}} =$

$= 2 \cdot \sqrt{ \dfrac{2}{5}} \cdot \sqrt{ \dfrac{2}{5}} - 5 \cdot \sqrt{ \dfrac{5}{8} } \cdot \sqrt{ \dfrac{2}{5}} + 4 \cdot \sqrt{ \dfrac{5}{2}} \cdot \sqrt{ \dfrac{2}{5}}$

$= 2 \cdot \dfrac{2}{5} - 5 \cdot \sqrt{ \dfrac{10}{40} } + 4 \cdot \sqrt{ \dfrac{10}{10}} = \dfrac{4}{5} - 5\sqrt{ \dfrac{1}{4} } + 4$

$= \dfrac{4}{5} - \dfrac{5}{2} + 4 = \dfrac{8 - 25 + 40}{10} = \bf \dfrac{23}{10}$