- Chapter 1- Rational and Irrational Numbers
- Chapter 2- Compound Interest [Without Using Formula
- Chapter 3- Compound Interest [Using Formula
- Chapter 4- Expansions
- Chapter 5- Factorisation
- Chapter 6- Simultaneous Equations
- Chapter 7- Indices [exponents]
- Chapter 8- Logarithms
- Chapter 9- Triangles [Congruency in Triangles]
- Chapter 10- Isosceles Triangle
- Chapter 11- Inequalities
- Chapter 12- Mid-Point and Its Converse
- Chapter 13- Pythagoras Theorem
- Chapter 14- Rectilinear Figures
- Chapter 15- Construction of Polygons
- Chapter 16- Area Theorems
- Chapter 17- Circles
- Chapter 18- Statistics
- Chapter 19- Mean and Median
- Chapter 20- Area and Perimeter of Plane Figures
- Chapter 21- Solids
- Chapter 22- Trigonometrical Ratios
- Chapter 23- Trigonometrical Ratios of Standard Angles
- Chapter 24- Solution Of Right Triangles
- Chapter 25- Complementary angles
- Chapter 26- Co-ordinate Geometry
- Chapter 27- Graphical Solution
- Chapter 28- Distance Formula
Selina Solutions Class 9 Mathematics Solutions for Exercise 1(C) in Chapter 1 - Chapter 1- Rational and Irrational Numbers
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Simplify:
(i) \frac{22}{2 \sqrt{3}+1}+\frac{17}{2 \sqrt{3}-1}
(ii) \frac{\sqrt{2}}{\sqrt{6}-\sqrt{2}}+\frac{\sqrt{3}}{\sqrt{6}+\sqrt{2}}
\begin{aligned} &\text { (i) }\\ &\begin{array}{l} \frac{22}{2 \sqrt{3}+1}+\frac{17}{2 \sqrt{3}-1} \\ \frac{22(2 \sqrt{3}-1)+17(2 \sqrt{3}+1)}{(2 \sqrt{3}+1)(2 \sqrt{3}-1)}=\frac{44 \sqrt{3}-22+34 \sqrt{3}+17}{(2 \sqrt{3})^{2}-1} \\ =\frac{78 \sqrt{3}-5}{12-1}=\frac{78 \sqrt{3}-5}{11} \end{array} \end{aligned}
\begin{aligned} &\text { (ii) }\\ &\begin{array}{l} \frac{\sqrt{2}}{\sqrt{6}-2}-\frac{\sqrt{3}}{\sqrt{6}+\sqrt{2}}=\frac{\sqrt{2}(\sqrt{6}+\sqrt{2})-\sqrt{3}(\sqrt{6}-\sqrt{2})}{(\sqrt{6})^{2}-(\sqrt{2})^{2}} \\ =\frac{\sqrt{12}+2-\sqrt{18}+\sqrt{6}}{6-2}=\frac{2 \sqrt{3}+2-3 \sqrt{2}+\sqrt{6}}{4} \end{array} \end{aligned}
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