Question:
If $x+1 / x=11$, find the value of $x^{2}+1 / x^{2}$
Solution:
We have, $x+1 / x=11$
Now, $(x+1 / x)^{2}=x^{2}+(1 / x)^{2}+2 * x * 1 / x$
$\Rightarrow(x+1 / x)^{2}=x / 2+1 / x^{2}+2$
$\Rightarrow(11)^{2}=x^{2}+1 / x^{2}+2[? x+1 / x=11]$
$\Rightarrow 121=x^{2}+1 / x^{2}+2$
$\Rightarrow x^{2}+1 / x^{2}=119$
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