Ridicam prima relatie la patrat:
[tex] (x+ \frac{1}{x}) ^{2} = x^{2} +2+ \frac{1}{ x^{2} } =25 => x^{2} + \frac{1}{ x^{2} }=23 [/tex]
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[tex](x+ \frac{1}{x})( x^{2} + \frac{1}{ x^{2} })= x^{3}+ (\frac{1}{x}+x)+ \frac{1}{ x^{3} } = x^{3}+ \frac{1}{ x^{3} }+5 [/tex]
[tex](x+ \frac{1}{x})( x^{2} + \frac{1}{ x^{2} } )=5*23=115[/tex]
[tex]( x^{3}+ \frac{1}{ x^{3} }+5=115 => x^{3}+ \frac{1}{ x^{3} }=110 [/tex]
