Question

Calculati media geometrica a numerelor:
a=√28-√20/√3+1 si b=√12+2/√7-√5

Multumesc!

Answer 1

...................................

Answer 2

        $a= \frac{\sqrt{28} - \sqrt{20}}{ \sqrt{3}+1 } =\frac{\sqrt{4*7} - \sqrt{4*5}}{ \sqrt{3}+1 }= \frac{2\sqrt{7} - 2\sqrt{5}}{ \sqrt{3}+1 }=\frac{2(\sqrt{7} - \sqrt{5})}{ \sqrt{3}+1 } \\ \\ b= \frac{ \sqrt{12}+2 }{ \sqrt{7}- \sqrt{5}}= \frac{ \sqrt{4*3}+2 }{ \sqrt{7}- \sqrt{5}}= \frac{2 \sqrt{3}+2 }{ \sqrt{7}- \sqrt{5}}=\frac{2 (\sqrt{3}+1) }{ \sqrt{7}- \sqrt{5}}$


$\\ \\ \text{Media geometrica este:} \\ \\ m_g= \sqrt{a*b} = \sqrt{\frac{2(\sqrt{7} - \sqrt{5})}{ \sqrt{3}+1}*\frac{2 (\sqrt{3}+1) }{ \sqrt{7}- \sqrt{5}}}= \sqrt{2*2} =\boxed{2}$