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Number systems — MATHS STD 9 — Question

Rajasthan BoardEnglish MediumSTD 9MATHSNumber systems1 Mark
Question
If $\text{x}=3+2\sqrt{2},$ than the value of $\text{x}+\frac{1}{\text{x}}$ is:
✓

Answer

  1. 6
    Solution:
    $\text{x}+\frac{1}{\text{x}}$
    $\Rightarrow\frac{\text{x}^2+1}{\text{x}}$
    Put the value of x,
    $\Rightarrow\frac{(3+2\sqrt{2})^2+1}{3+2\sqrt{2}}$
    $\Rightarrow\frac{9+8+12\sqrt{2}+1}{3+2\sqrt{2}}$
    $\Rightarrow\frac{18+12\sqrt{2}}{3+2\sqrt{2}}$
    $\Rightarrow\frac{6(3+2\sqrt{2})}{3+2\sqrt{2}}$
    $\Rightarrow6$

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