Question

Daca a/5-√3=5+√3/b atunci media geometrica a numerelor a si b este egala cu ..................

Answer 1

a/(5-√3)=(5+√3)/b
ab=(5-√3)(5+√3)=25-9=16
√ab=√16=4

Answer 2

$\it \dfrac{a}{5-\sqrt3} = \dfrac{5+\sqrt3}{b} \Leftrightarrow ab=(5-\sqrt3)(5+\sqrt3)\Leftrightarrow ab =5^2-(\sqrt3)^2$

$\Leftrightarrow \it ab = 25 -3 \Leftrightarrow ab = 23$

$\it m_a =\sqrt{ab} =\sqrt{23}$