Question

Daca  x∈R cu steluta , astfel incat $x+ \frac{1}{x} =4, atunci aflati valoarea sumei x^{2} + \frac{1}{ x^{2} }$

Answer 1

$x+ \frac{1}{x} =4$

ridicam la patrat;

$(x+ \frac{1}{x} )^2=4^2$

$x^{2} + \frac{1}{ x^{2} } +2*x* \frac{1}{x} =16$

$x^{2} + \frac{1}{ x^{2} } +2=16$

$x^{2} + \frac{1}{ x^{2} } =14$