If m find i m ii n iii mn

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

Question 7 Exercise 1(C)

If m $=\frac{1}{3-2 \sqrt{2}} \text { and } n=\frac{1}{3+2 \sqrt{2}}$ find:

(i) m²

(ii) n²

(iii) mn

Answer:

$\begin{array}{l} \begin{aligned} \text { (i) } m &=\frac{1}{3-2 \sqrt{2}} \\ =& \frac{1}{3-2 \sqrt{2}} \times \frac{3+2 \sqrt{2}}{3+2 \sqrt{2}} \\ =& \frac{3+2 \sqrt{2}}{(3)^{2}-(2 \sqrt{2})^{2}} \\ =& \frac{3+2 \sqrt{2}}{9-8} \\ =3 &+2 \sqrt{2} \\ \rightarrow m^{2}=(3+2 \sqrt{2})^{2} \\ =(3)^{2}+2 \times 3 \times 2 \sqrt{2}+(2 \sqrt{2})^{2} \\ =9+12 \sqrt{2}+8 \\ =17+12 \sqrt{2} \end{aligned} \end{array}$

$\begin{aligned} &\langle\|) \cap=\frac{1}{3+2 \sqrt{2}}\\ &\begin{array}{l} =\frac{1}{3+2 \sqrt{2}} \times \frac{3-2 \sqrt{2}}{3-2 \sqrt{2}} \\ =\frac{3-2 \sqrt{2}}{(3)^{2}-(2 \sqrt{2})^{2}} \\ =\frac{3+2 \sqrt{2}}{9-8} \\ =3-2 \sqrt{2} \\ \begin{aligned} -n^{2} &=(3-2 \sqrt{2})^{2} \\ &=(3)^{2}-2 \times 3 \times 2 \sqrt{2}+(2 \sqrt{2})^{2} \\ &=9-12 \sqrt{2}+8 \\ &=17-12 \sqrt{2} \end{aligned} \end{array} \end{aligned}$

$\text { (iii) } m n=(3+2 \sqrt{2})(3-2 \sqrt{2})=(3)^{2}-(2 \sqrt{2})^{2}=9-8=1$

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