Question
If $x+\frac{1}{x}=3 ;$ find $x^2+\frac{1}{x^2}$
✓
Answer
$\left(x+\frac{1}{x}\right)^2 $
$ =x^2+\frac{1}{x^2}+2(x)\left(\frac{1}{x}\right) $
$ \Rightarrow(3)^2 $
$ =x^2+\frac{1}{x^2}+2$
$\Rightarrow x^2+\frac{1}{x^2}$
$=9-2 $
$ =7 .$
$ =x^2+\frac{1}{x^2}+2(x)\left(\frac{1}{x}\right) $
$ \Rightarrow(3)^2 $
$ =x^2+\frac{1}{x^2}+2$
$\Rightarrow x^2+\frac{1}{x^2}$
$=9-2 $
$ =7 .$
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