Question

Daca $x+ \frac{1}{x} =5$, atunci $x^{2} + \frac{1}{ x^{2} } =....$

Answer 1

Ridicind la patrat obtinem : $(x+ \frac{1}{x}) ^{2} =25 <=> x^{2} +2*x* \frac{1}{x}+ \frac{1}{ x^{2} } =25<=> x^{2} + 2+ \frac{1}{ x^{2} } =>$ $x^{2} + \frac{1}{ x^{2} } =25-2=23$

Answer 2

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]