- 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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.If \frac{2+\sqrt{5}}{2-\sqrt{5}}=x \text { and } \frac{2-\sqrt{5}}{2+\sqrt{5}}=y find the value of x²-y².
\begin{aligned} x=\frac{2+\sqrt{5}}{2-\sqrt{5}} &=& \frac{2-\sqrt{5}}{2+\sqrt{5}} \\ =& \frac{2+\sqrt{5}}{2-\sqrt{5}} \times \frac{2+\sqrt{5}}{2+\sqrt{5}} &=\frac{2-\sqrt{5}}{2+\sqrt{5}} \times \frac{2-\sqrt{5}}{2-\sqrt{5}} \\ =& \frac{(2+\sqrt{5})^{2}}{2^{2}-(\sqrt{5})^{2}} &=\frac{(2-\sqrt{5})^{2}}{2^{2}-(\sqrt{5})^{2}} \\ -\frac{4+4 \sqrt{5}+5}{4-5} &-\frac{4-4 \sqrt{5}+5}{4-5} \\ =\frac{9+4 \sqrt{5}}{-1} &=\frac{9-4 \sqrt{5}}{-1} \\ =-9-4 \sqrt{5} &=-9+4 \sqrt{5} \\ \therefore x^{2}-y^{2}=&(-9-4 \sqrt{5})^{2}-(-9+4 \sqrt{5})^{2} \\ &=81+72 \sqrt{5}+80-(81-72 \sqrt{5}+80) \\ &=81+72 \sqrt{5}+80-81+72 \sqrt{5}-80 \\ &-144 \sqrt{5} \end{aligned}
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