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Number systems — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsNumber systems1 Mark
MCQ
$\frac{1}{\big(3+2\sqrt{2}\big)}=?$
  • A
    $\frac{3-2\sqrt{2}}{17}$
  • B
    $\frac{\big(3-2\sqrt{2}\big)}{13}$
  • C
    $\big(3-2\sqrt{2}\big)$
  • D
    None of these.
✓

Answer

  1. $\big(3-2\sqrt{2}\big)$
    Solution:
    $\frac{1}{\big(3+2\sqrt{2}\big)}=\frac{1}{3+2\sqrt{2}}\times\frac{3-2\sqrt{2}}{3-2\sqrt{2}}$
    $=\frac{3-2\sqrt{2}}{3^2-\big(2\sqrt{2}\big)^2}$
    $=\frac{3-2\sqrt{2}}{9-8}$
    $=\big(3-2\sqrt{2}\big)$
    Hence, the correct option is (c).

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