Question

$Daca \\ a + \frac{1}{a} = 4 \\ atunci \\ a^{2} + \frac{1}{ a^{2} } = ?$

Answer 1

E=(a+1/a)²-2·a·1/a=4²-2=14

Answer 2

 [tex]a+\frac{1}{a}=4\;\;ridicam\;la\;patrat\;ambele\;parti\;al\;egalitatii ...\\ vom\;avea:\;a^2+2\cdot\not{a}\cdot\frac{1}{\not{a}}+\frac{1}{a^2}=16\;de\;unde\;...\\ a^2+\frac{1}{a^2}=16-2=14[/tex]