If $x + \dfrac{1}{x} = 5$, find $x^{2} + \dfrac{1}{x^{2}}$.
If $x + \dfrac{1}{x} = 5$, find $x^{2} + \dfrac{1}{x^{2}}$.
- $23$
- $25$
- $27$
- $21$
Solution
$\left(x+\dfrac{1}{x}\right)^{2} = x^{2} + 2 + \dfrac{1}{x^{2}} = 25 \Rightarrow x^{2}+\dfrac{1}{x^{2}} = 23$.
Asked in: IMO
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