Question

media geometrica a nr a=(√3-√2)(√9-√5), b=(√3+√2)(√9+√5)

Answer 1

$\it m_g=\sqrt{a\cdot b}=\sqrt{(\sqrt3-\sqrt2)(\sqrt9-\sqrt5)(\sqrt3+\sqrt2)(\sqrt9+\sqrt5)}=\\ \\ =\sqrt{(\sqrt3-\sqrt2)(\sqrt3+\sqrt2)(\sqrt9-\sqrt5)(\sqrt9+\sqrt5)}=\\ \\ =\sqrt{[(\sqrt3)^2-(\sqrt2)^2][(\sqrt9)^2-(\sqrt5)^2]}=\sqrt{1\cdot4}=2$