Răspuns :
[tex](x+ \frac{1}{x} ) ^{2} = x^{2} + 2+\frac{1}{ x^{2} } \\ x^{2} +\frac{1}{ x^{2} } = 25-2=23 \\ \\ (x+ \frac{1}{x} ) ^{3}= x^{3} + \frac{1}{ x^{3} } + 3(x+ \frac{1}{x} ) \\ x^{3} + \frac{1}{ x^{3} }=125-15=110 \\ \\ ( x^{2} +\frac{1}{ x^{2} } )^{2}=x^{4} + 2+\frac{1}{ x^{4} } \\ x^{4} +\frac{1}{ x^{4} }=529-2=527 \\ \\ E=x +\frac{1}{ x }+x^{2} +\frac{1}{ x^{2} }+x^{3} +\frac{1}{ x^{3} }+x^{4} +\frac{1}{ x^{4} } \\ E=5+23+110+527=665[/tex]
