[tex]x+ \frac{1}{x}=5 [/tex], ridicam egalitatea la patrat, obtinem :
[tex] x^{2} +2*x* \frac{1}{x}+ \frac{1}{ x^{2} }=25,adica,x^{2} +2+ \frac{1}{ x^{2} } =25,sau, x^{2} +\frac{1}{ x^{2} }=23,[/tex] ridicand din nou la patrat, se obtine: [tex] x^{4} +2 x^{2} * \frac{1}{ x^{2} } + \frac{1}{ x^{4} } =529,sau, x^{4} +2+ \frac{1}{ x^{4} } =527,deci: x^{4} + \frac{1}{ x^{4} }=525 [/tex]
