Question

Calculati:

[tex] \frac{1}{x ^{2} } + x^{2} = ?
[/tex]

Stiind ca:

$\frac{1}{x} +x = 10$

Answer 1

[tex]x+\dfrac{1}{x}=10\\ \text{Ridicand la patrat obtinem:}\\ \left(x+\dfrac{1}{x}\right)^2=10^2\\ x^2+2\cdot \not x\cdot \dfrac{1}{\not x}+ \dfrac{1}{x^2}=100\\ x^2+2+\dfrac{1}{x^2}=100\\ \boxed{x^2+\dfrac{1}{x^2}=98}[/tex]