Question

Sa se arate ca: $\frac{\sqrt{6} }{\sqrt{8}+\sqrt{10} } + \frac{\sqrt{8} }{\sqrt{6}+\sqrt{10} } + \frac{\sqrt{10} }{\sqrt{6}+\sqrt{8} } \ \textless \ 2$.

Answer 1

Bună!

$\sqrt{3} ~$ ≈ 1,73

$\sqrt{5}$ ≈ 2,23

$-3\sqrt{3} +3\sqrt{5} =3(\sqrt{5} -\sqrt{3} )=3(2,23-1,73)=3*0,5=1,5$

1,5<2 ⇒ $-3\sqrt{3} +3\sqrt{5} < 2$ (A)