Question

Stiind ca x+1/x=-2. Aratati ca x la 2 +1/x la 2 =2

Answer 1

$x + \frac{1}{x}= -2 \\ \\ (x + \frac{1}{x})^{2}= (-2)^{2} =\ \textgreater \ x^{2} + 2* x* \frac{1}{x}+\frac{1}{x^{2}} = 4 =\ \textgreater \ x^{2} + 2 + \frac{1}{x^{2}}= 4 =\ \textgreater \ \\ \\ x^{2} + \frac{1}{x^{2}} = 4-2= 2.$

Answer 2

[tex]\it x+\dfrac{1}{x} =-2 \Rightarrow \left(x+\dfrac{1}{x} \right)^2 =(-2)^2 \Rightarrow x^2+2\cdot x\cdot\dfrac{1}{x} +\dfrac{1}{x^2} =4 \Rightarrow \\\;\\ \\\;\\ \Rightarrow x^2+2+\dfrac{1}{x^2} =4 |_{-2} \Rightarrow x^2+\dfrac{1}{x^2} =2.[/tex]