Question

Ajuuuuutor, am nevoie uuuurgent​

Answer 1

$\displaystyle \frac1a+\frac1b=\frac1{\sqrt7-\sqrt2}+\frac1{\sqrt7+\sqrt2}=\frac{\sqrt7+\sqrt2}{(\sqrt7+\srqt2)(\sqrt7-\sqrt2)}+\frac{\sqrt7-\sqrt2}{(\sqrt7-\sqrt2)(\sqrt7+\sqrt2)}=\\=\frac{\sqrt7+\sqrt2+\sqrt7-\sqrt2}{(\sqrt7)^2-(\sqrt2)^2}=\frac{2\sqrt7}{5}$

Verificam ca apartine intervalului:

$\displaystyle\frac1a+\frac1b\in\left(\frac45, \frac65\right)\Rightarrow\frac45<\frac1a+\frac1b<\frac65\\\\\frac45<\frac{2\sqrt7}5<\frac65\:\Big|\cdot5\\\\4<2\sqrt7<6\:\Big|:2\\2<\sqrt7<3\: (A)\Rightarrow \frac1a+\frac1b\in\left(\frac45, \frac65\right)$