Question

Daca x+1 supra x = 5 ,atunci x la puterea 2 + 1 supra x la puterea 2 este...?

Answer 1

$x+ \frac{1}{x} =5 \\ \\ (x+ \frac{1}{x})^2=5^2 \\ \\ x^{2} +2*x* \frac{1}{x}+ \frac{1}{x^2} =25 \\ \\ x^{2} +2+ \frac{1}{x^2} =25 \\ \\ \boxed{ \bold{x^{2} + \frac{1}{x^2}=23 }}$

Answer 2

$x+ \frac{1}{x}=5 \\ (x+ \frac{1}{x})^2= x^2+ \frac{1}{x^2}+2 \\ 5^2= x^2+ \frac{1}{x^2}+2 =\ \textgreater \ x^2+ \frac{1}{x^2}=23$