Question

Daca$x+ \frac{1}{x} =5$ sa se calculeze cat este x² +1pe x²

Answer 1

[tex]x+\dfrac{1}{x}=5 |()^2\\ \left(x+\dfrac{1}{x}\right)^2=25\\ x^2+2\cdot\not x\cdot \dfrac{1}{\not x}+\dfrac{1}{x^2}=25\\ x^2+2+\dfrac{1}{x^2}=25\\ \boxed{x^2+\dfrac{1}{x^2}=23}[/tex]