Question

Ex 11 vaa rog dau coroana

Answer 1

$\displaystyle a=5 \sqrt{6} -6 \sqrt{24} +7 \sqrt{54} -8 \sqrt{96} +9 \sqrt{150} \\ \\ a=5 \sqrt{6} -6 \cdot 2 \sqrt{6} +7 \cdot 3 \sqrt{6} -8 \cdot 4 \sqrt{6} +9 \cdot 5 \sqrt{6} \\ \\ a=5 \sqrt{6} -12 \sqrt{6} +21 \sqrt{6} -32 \sqrt{6} +45 \sqrt{6} \\ \\ a=27 \sqrt{6}$
$\displaystyle b=\left(2 \sqrt{3} -3 \sqrt{12} +4 \sqrt{27} -7 \sqrt{3} +3 \sqrt{75} \right)\cdot \sqrt{2} \\ \\ b=\left(2 \sqrt{3} -3 \cdot 2 \sqrt{3} +4 \cdot 3 \sqrt{3} -7 \sqrt{3} +3 \cdot 5 \sqrt{3} \right)\cdot \sqrt{2} \\ \\ b=\left(2 \sqrt{3} -6 \sqrt{3} +12 \sqrt{3} -7 \sqrt{3} +15 \sqrt{3} \right) \cdot \sqrt{2} \\ \\ b=16 \sqrt{3} \cdot \sqrt{2} \\ \\ b= 16 \sqrt{6}$
$\displaystyle m_a= \frac{a+b}{2} = \frac{27 \sqrt{6}+16 \sqrt{6} }{2} = \frac{43 \sqrt{6} }{2} \\ \\ m_g= \sqrt{a \cdot b} = \sqrt{27 \sqrt{6} \cdot 16 \sqrt{6} } = \sqrt{432 \cdot 6} = \sqrt{2592} =36 \sqrt{2}$