Selina Solutions Class 9 Mathematics Solutions for Exercise 1(C) in Chapter 1 - Chapter 1- Rational and Irrational Numbers

Question 8 Exercise 1(C)

If 𝒙 = 𝟐√𝟑 + 𝟐√𝟐, find:

(I) $\frac{1}{x}$

(ii) 𝒙 + $\frac{1}{x}$

(iii) (𝒙 + $\frac{1}{x}$ )²

Answer:

$\begin{aligned} &\text { (i) }\\ &\frac{1}{x}-\frac{1}{2 \sqrt{2}+2 \sqrt{2}} \times \frac{2 \sqrt{3}-\sqrt{2}}{2 \sqrt{3}-2 \sqrt{2}}-\frac{2 \sqrt{3}-2 \sqrt{2}}{12-8}\\ &=\frac{2\{\sqrt{3}-\sqrt{2})}{42}=\frac{\sqrt{3}-\sqrt{2}}{2} \end{aligned}$

$\begin{aligned} &\text { (ii) }\\ &x+\frac{1}{x}=2 \sqrt{-}+2 \sqrt{2}+\frac{\sqrt{3}-\sqrt{2}}{2}\\ &-2 i \sqrt{3}+\sqrt{2} i+\frac{(\sqrt{3}-\sqrt{2})}{2}\\ &=\frac{4(\sqrt{3}+\sqrt{2})+(\sqrt{3}-\sqrt{2})}{2}\\ &-\frac{4 \sqrt{3}+4 \sqrt{2}+\sqrt{3}-\sqrt{2}}{2}\\ &=\frac{5 \sqrt{3}+3 \sqrt{2}}{2} \end{aligned}$

$\begin{aligned} &\text { (iii) }\\ &\left(x+\frac{1}{x}\right)=\left(\frac{E \sqrt{3}+3 \sqrt{2}}{2}\right)=\frac{75+18+30 \sqrt{8}}{4}\\ &=\frac{93+30 \sqrt{6}}{4} \end{aligned}$

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