Question

va rog ajutatima si pe mn​

Answer 1

$\it \Big(x+\dfrac{1}{x}\Big)^2=6^2 \Rightarrow x^2+2\cdot x\cdot\dfrac{1}{x}+\dfrac{1}{x^2}=36 \Rightarrow x^2+2+\dfrac{1}{x^2}=36|_{-2} \Rightarrow \\ \\ \\ \Rightarrow x^2+\dfrac{1}{x^2}=34\ \ \ \ \ (1)\\ \\ \\ 2\cdot x\cdot\dfrac{1}{x}=2\ \ \ \ \ (2)\\ \\ \\ (1),\ (2) \Rightarrow x^2+\dfrac{1}{x^2}-2\cdot x\cdot\dfrac{1}{x}=34-2 \Rightarrow \Big(x-\dfrac{1}{x}\Big)^2=32 \Rightarrow$

$\it \Rightarrow \sqrt{\Big(x-\dfrac{1}{x}\Big)^2}=\sqrt{32} \Rightarrow |x-\dfrac{1}{x}|=\sqrt{16\cdot2}\Rightarrow x-\dfrac{1}{x}=\pm4\sqrt2$