Question

Calculati $x^{2}$ + $\frac{1} x^{2}$ , stiind că $x + \frac{1}{x} = 3$ unde x ∈ $R ^{*}$

Answer 1

[tex]x+ \frac{1}{x}=3 \\ x^{2} + \frac{1}{ x^{2} } =? \\ \\ (x +\frac{1}{x}) ^{2} =(3) ^{2} \\ x^{2} +2*x* \frac{1}{x}+ \frac{1}{ x^{2} } =9 \\ x^{2} +2+ \frac{1}{x^2}=9 \\ x^{2} + \frac{1}{ x^{2} } = 9-2 \\ x^{2} + \frac{1}{ x^{2} } =7 [/tex]