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Calculati [tex] x^{2} + \frac{1}{ x^{2} } stiind ca x + \frac{1}{x} =3[/tex]

Răspuns :

x+[tex] \frac{1}{x} [/tex]=3 ridicam toata ecuatia la puterea a2a si avem asa:
(x+[tex] \frac{1}{x} [/tex])²=9
x²+[tex] \frac{1}{ x^{2} } [/tex]+1=9
=> x² + [tex] \frac{1}{ x^{2} } [/tex]=8