Question

VA ROG !!! Daca puteti sa imi si explicati1) Rezolvarea calculului (2 supra √2 - 3 supra√3)·√6 + (3supra√18 - 10 supra√75 )(-√6) este egal cu... 
2) Media geometrica a numerelor a=|2√7-8| si b=|2√7+8| este egala cu...

Answer 1

1)
($\frac{2}{ \sqrt{2} }$-$\frac{3}{ \sqrt{3} }$)⇒$( \frac{2}{ \sqrt{2} } - \frac{3}{ \sqrt{3} })( \sqrt{6} - \frac{ \sqrt{3} }{18}- \frac{10}{ \sqrt{75}})( \sqrt{6})= \sqrt{6}( \frac{2}{ \sqrt{2}}- \frac{3}{ \sqrt{3} } - \frac{3}{ \sqrt{18}}- \frac{10}{ \sqrt{10}})=$$=( \frac{2}{ \sqrt{2} }- \frac{3}{ \sqrt{3} } - \frac{3}{3 \sqrt{3} } + \frac{10}{5 \sqrt{3}} )= \sqrt{6}( \frac{1}{ \sqrt{2} } - \frac{1}{ \sqrt{3} })= \frac{ \sqrt{6} }{ \sqrt{2} } - \frac{ \sqrt{6} }{ \sqrt{3} }= \sqrt{3} - \sqrt{2}$

2) a=|2$\sqrt{7}$-8|
2$\sqrt{7}$=$\sqrt{28}$
$\sqrt{28} \geq \sqrt{64}$⇒a=$2 \sqrt{7}+8$
b=$2 \sqrt{7}+8$

Mg=$\sqrt{(8-2 \sqrt{7})(8+2 \sqrt{7})}= \sqrt{8 ^{2} -(2 \sqrt{7)^{2}}}= \sqrt{16-14}= \sqrt{2}$