Aplici formula :
[tex] (a+b)^{2} = a^{2} + b^{2} +2*a*b[/tex]
unde a=x si b=1/x si obtii:
[tex] (x+ \frac{1}{x} )^{2} = x^{2} + ( \frac{1}{x} )^{2} +2*x* \frac{1}{x} =[/tex]
=[tex]x^{2} + \frac{1}{ x^{2} } +2[/tex]
Deci:
[tex] 3^{2} =(x^{2} + \frac{1}{ x^{2} })+2[/tex]
[tex] 9 =(x^{2} + \frac{1}{ x^{2} })+2[/tex]
[tex] x^{2} + \frac{1}{ x^{2} } =9-2=7[/tex]
