Question

Stiind ca a+1/a=4 a diferit de 0, calculeaza a la a2 + 1/a la a 2 .mersi

Answer 1

$a+ \frac{1}{a}=4 \\ \\ (a+ \frac{1}{a})^2=4^2 \\ \\ a^2+2 \cdot a \cdot \frac{1}{a}+ \frac{1}{a^2} =16 \\ \\ a^2+ 2+\frac{1}{a^2} =16 \\ \\ a^2+ \frac{1}{a^2}=16-2 \\ \\ \boxed{a^2+ \frac{1}{a^2}=14 }$