Question

Dau 14 puncte celui care ma ajuta sa rezolv calculu:
Calculati media geometrica a umerelor a=| $4\sqrt{6} - 7\sqrt{2} |$ si b =$| 4 \sqrt{6} + 7\sqrt{2} |$

Answer 1

$m_{g} = \sqrt{a*b}$
$4 \sqrt{6}-7 \sqrt{2} = \sqrt{ 4^{2}*6} - \sqrt{ 7^{2}*2}= \sqrt{16*6} - \sqrt{49*2} = \sqrt{96} - \sqrt{98}$, deci
$a=7 \sqrt{2} -4 \sqrt{6}$
$a*b=(7 \sqrt{2} -4 \sqrt{6} )(7 \sqrt{2} +4 \sqrt{6})$
folosim formula : $(a-b)(a+b)= a^{2} -b^{2}$
$a*b=(7 \sqrt{2} ) ^{2} -(4 \sqrt{6} ) ^{2} =98-96=2 \\ m_{g} = \sqrt{a*b} = \sqrt{2}$