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Integration of Piecewise Continuous Functions

If x + 1x =...

Question

If $x + \frac{1}{x} = 3$ , then the value of $[x^{2} + \frac{1}{x^{2}}]$ is

A

32

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B

6

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C

7

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D

113

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Solution

The correct option is C 7
$\begin{matrix} W e h a v e x + \frac{1}{x} = 3 N o w {[x + \frac{1}{x}]}^{2} = x^{2} + \frac{1}{x^{2}} + 2 3^{2} = x^{2} + \frac{1}{x^{2}} + 2 x^{2} + \frac{1}{x^{2}} = 9 - 2 x^{2} + \frac{1}{x^{2}} = 7 \end{matrix}$
Hence, the option $C$ is the correct answer.

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