Question:
Tick (✓) the correct answer:
If $\left(x+\frac{1}{x}\right)=5$, then $\left(x^{2}+\frac{1}{x^{2}}\right)=?$
(a) 25
(b) 27
(c) 23
(d) $25 \frac{1}{25}$
Solution:
(c) 23
$\left(x+\frac{1}{x}\right)=5$
$\Rightarrow$ Squaring both the sides :
$\Rightarrow\left(x+\frac{1}{x}\right)^{2}=(5)^{2}$
$\Rightarrow\left(x^{2}+\frac{1}{x^{2}}+2(x)\left(\frac{1}{x}\right)\right)=25$
$\Rightarrow\left(x^{2}+\frac{1}{x^{2}}\right)+2=25$
$\Rightarrow\left(x^{2}+\frac{1}{x^{2}}\right)=25-2$
$\Rightarrow\left(x^{2}+\frac{1}{x^{2}}\right)=23$
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