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Daca [tex]x+ \frac{1}{x} =5[/tex], atunci [tex] x^{2} + \frac{1}{ x^{2} } =....[/tex]

Răspuns :

Danutghenghea1ask
Ridicind la patrat obtinem : [tex](x+ \frac{1}{x}) ^{2} =25 <=> x^{2} +2*x* \frac{1}{x}+ \frac{1}{ x^{2} } =25<=> x^{2} + 2+ \frac{1}{ x^{2} } =>  [/tex] [tex] x^{2} + \frac{1}{ x^{2} } =25-2=23[/tex]
Ridica prima fractie la puterea a doua in ambele parti.
[tex]x+ \frac{1}{x} = 5 \\ x^{2} + \frac{2x}{x} + \frac{1}{ x^{2} } = 5^{2} \\ x^{2} + 2 + \frac{1}{ x^{2} } = 25 \\ x^{2} + \frac{1}{ x^{2} } = 23 [/tex]