Question

Sa se calculeze x² + $\frac{1}{x ^{2} }$ , stiind ca x- $\frac{1}{x}$ = 6

Answer 1

Ridicam la patrat ecuatia data:

$\left(x-\dfrac1x\right)^2=6 ^2\Rightarrow x^2-2\cdot x\cdot\dfrac1x+\dfrac{1}{x^2}=36\Rightarrow x^2+\dfrac{1}{x^2}=38$