Question

Найдите значение дроби a5+a2/a2-a+1 при a = -1/3

Answer 1

$\displaystyle\bf\\\frac{a^{5}+a^{2} }{a^{2}-a+1 }=\frac{a^{2}\cdot(a^{3}+1) }{a^{2}-a+1 } =\frac{a^{2}\cdot(a+1)\cdot(a^{2}-a+1) }{a^{2} -a+1}=a^{2}\cdot(a+1) \\\\\\a=-\frac{1}{3} \\\\\\a^{2} \cdot(a+1)=\Big(-\frac{1}{3}\Big)^{2} \cdot\Big(-\frac{1}{3}+1\Big)= \frac{1}{9}\cdot\frac{2}{3}=\frac{2}{27}$