Question

Buna! Puteti rezolva acest exercițiu? am nevoie ​

Answer 1

Explicație pas cu pas:

a)

$a = \frac{ \sqrt{6} }{5} \Big( \frac{1}{ \sqrt{2} } + \frac{2}{3 \sqrt{2} } \Big) + \frac{5}{ \sqrt{3} } = \frac{ \sqrt{6} }{ 5\sqrt{2} } + \frac{2 \sqrt{6} }{15 \sqrt{2} } + \frac{5 \sqrt{3} }{3} = \frac{ \sqrt{3} }{5} + \frac{2 \sqrt{3} }{15} + \frac{5 \sqrt{3} }{3} = \frac{3 \sqrt{3} + 2 \sqrt{3} + 25 \sqrt{3} }{15} = \frac{30 \sqrt{3} }{15} = \bf 2 \sqrt{3}$

$b = \frac{13}{ \sqrt{3} } + \Big( \frac{1}{ \sqrt{2} } - \frac{2}{3 \sqrt{2} } \Big) : \frac{1}{ 5\sqrt{6} } = \frac{13 \sqrt{3} }{3} + \Big( \frac{1}{ \sqrt{2} } - \frac{2}{3 \sqrt{2} } \Big) \cdot 5\sqrt{6} = \frac{13 \sqrt{3} }{3} + 5 \sqrt{3} - \frac{10 \sqrt{3} }{3} = \frac{3 \sqrt{3} }{3} + 5 \sqrt{3} = \sqrt{3} + 5 \sqrt{3} = \bf 6 \sqrt{3}$

b)

$m_{g} = \sqrt{ab} = \sqrt{2 \sqrt{3} \cdot 6 \sqrt{3} } = \sqrt{ {6}^{2} } = \bf 6$