Question

Se considera numarul x apartine R* Daca X-1/x = 4 , calculati x^2 + 1/x^2​

Answer 1

Salut,

$x-\dfrac{1}x=4\ (\ )^2\Rightarrow\left(x-\dfrac{1}x\right)^2=16\Leftrightarrow x^2-2\cdot x\cdot\dfrac{1}x+\left(\dfrac{1}x\right)^2=16\Leftrightarrow\\\\\Leftrightarrow x^2-2+\dfrac{1}{x^2}=16,\ deci\ \boxed{x^2+\dfrac{1}{x^2}=18.}$

Green eyes.