Question
Simplify:$\left(a-\frac{1}{a}\right)^2+\left(a+\frac{1}{a}\right)^2$
✓
Answer
$\left(a-\frac{1}{a}\right)^2+\left(a+\frac{1}{a}\right)^2$
$=(a)^2+\left(\frac{1}{a}\right)^2-2(a)\left(\frac{1}{a}\right)+(a)^2+\left(\frac{1}{a}\right)^2+2(a)\left(\frac{1}{a}\right) $
$ =a^2+\frac{1}{a^2}-2+a^2+\frac{1}{a^2}+2 $
$=2 a^2+\frac{2}{a^2} .$
$=(a)^2+\left(\frac{1}{a}\right)^2-2(a)\left(\frac{1}{a}\right)+(a)^2+\left(\frac{1}{a}\right)^2+2(a)\left(\frac{1}{a}\right) $
$ =a^2+\frac{1}{a^2}-2+a^2+\frac{1}{a^2}+2 $
$=2 a^2+\frac{2}{a^2} .$
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