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daca x+[tex] \frac{1}{x} =3 [/tex] calculati [tex] x^{4} [/tex]+ [tex] \frac{1}{ x^{4} } [/tex]

Răspuns :

[tex]x+\frac{1}{x}=3|*()^2\\ x^2+2+\frac{1}{x^2}=9\\ x^2+\frac{1}{x^2}=7|*()^2\\ x^4+2+\frac{1}{x^4}=49\\ x^4+\frac{1}{x^4}=47[/tex]