Question

stiind ca x+1/2=-2,unde x este numar real,aratati ca xla puterea 2 +1/× la puterea 2 =2

Answer 1

$x+ \dfrac{1}{x} = -2 \Big|^2 \Rightarrow \Big(x+ \dfrac{1}{x}\Big)^2 = (-2)^2 \Rightarrow x^2+2\cdot x\cdot \dfrac{1}{x}+\Big( \dfrac{1}{x}\Big)^2 = 4 \Rightarrow \\ \\ \Rightarrow x^2+2 + \dfrac{1}{x^2} =4 \Rightarrow x^2+ \dfrac{1}{x^2} = 4-2 \Rightarrow \boxed{x^2+\dfrac{1}{x^2}=2}$