Question

rezolvati exercitile 2,3

Answer 1

Explicație pas cu pas:

2.

$m_{g} = \sqrt{x \cdot y} \iff 30 = \sqrt{x \cdot 3 \sqrt{15} }$

$x \cdot 3 \sqrt{15} = 900$

$x = \dfrac{900}{3 \sqrt{15} } = \dfrac{300 \sqrt{15} }{15} = 20 \sqrt{15}$

3.

$x = \dfrac{9}{ \sqrt{28} } - \dfrac{1}{ \sqrt{7} } = \dfrac{9}{ 2\sqrt{7} } - \dfrac{1}{ \sqrt{7} } = \\ = \dfrac{9 \sqrt{7} - 2 \sqrt{7} }{14} = \dfrac{7 \sqrt{7}}{14} = \dfrac{\sqrt{7}}{2}$

$y = \dfrac{7}{3} \bigg( \dfrac{5}{2 \sqrt{7} } + \dfrac{8}{ \sqrt{7} } \bigg) = \dfrac{7}{3} \cdot \dfrac{5 \sqrt{7} + 16 \sqrt{7} }{14} = \\ = \dfrac{1}{3} \cdot \dfrac{21 \sqrt{7}}{2} = \dfrac{7 \sqrt{7}}{2}$

$m_{g} = \sqrt{x \cdot y} = \sqrt{\dfrac{\sqrt{7}}{2} \cdot \dfrac{7\sqrt{7}}{2}} = \sqrt{\dfrac{ {7}^{2} }{ {2}^{2} }} = \dfrac{7}{2}$