Question

stiind ca x+1/x=-2,unde x este numar real neutru,aratati ca x^2+1/x^2=2

Answer 1

Salut,

$\left(x+\dfrac{1}x\right)^2=x^2+2\cdot x\cdot\dfrac{1}x+\dfrac{1}{x^2}=x^2+2+\dfrac{1}{x^2}\Rightarrow\\\\\Rightarrow x^2+\dfrac{1}{x^2}=\left(x+\dfrac{1}x\right)^2-2=(-2)^2-2=4-2=2.$

Ceea ce trebuia demonstrat.

Green eyes.

Answer 2

[tex]\it x +\dfrac{1}{x} =-2 \Rightarrow x^2 +1 = -2x \Rightarrow x^2+2x+1 =0 \Rightarrow (x+1)^2 =0 \Rightarrow \\\;\\ \\\;\\ \Rightarrow x+1 = 0\Rightarrow x = -1[/tex]

$\it x^2+\dfrac{1}{x^2} = (-1)^2+\dfrac{1}{(-1)^2} =1+1 =2$