Question

Stiind ca a+1/a=5/2 unde a este numar real nenul aratati ca a patrat +1/a patrat =17/4

Answer 1

[tex] a+ \frac{1}{a} = \frac{5}{2} \\ (a+ \frac{1}{a})^2 =( \frac{5}{2} )^2\\ a+2\cdot a \cdot\frac{1}{a}+ \frac{1}{a^2} = \frac{25}{4} \\ a+2+ \frac{1}{a^2}=\frac{25}{4}\\ a+\frac{1}{a^2}=\frac{25}{4}-2\\ a+\frac{1}{a^2}=\frac{25}{4}- \frac{8}{4} \\ a+\frac{1}{a^2}=\frac{17}{4}[/tex]