Question

Se x+1/x = 57, calcule x² + 1/x².

Answer 1

$x+\dfrac{1}{x}=57 \\ \\ \left( x+\dfrac{1}{x}\right)^2=57^2 \\ \\ x^2 + 2x\dfrac{1}{x}+\left( \dfrac{1}{x} \right)^2 = 3249 \\ \\ x^2 + 2+\left( \dfrac{1}{x} \right)^2 = 3249 \\ \\ \boxed{x^2 +\left( \dfrac{1}{x} \right)^2 = 3247}$