Question

Stiind ca x+$\frac{1}{x} =3$ calculati x²+$\frac{1}{ x^{2} }$ ; x∈ R

Answer 1

$(x+ \frac{1}{x}) ^{2} = x^{2} + \frac{1}{x^{2} } + 2*x* \frac{1}{x} = x^{2} + \frac{1}{x^{2} } + 2 = 3 + 2 = 5$ 
[/tex]} = [tex] (x+ \frac{1}{x}) ^{2} - 2*x* \frac{1}{x} = 5 - 3 = 2