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Selina Solutions Class 9 Mathematics Solutions for Exercise 1(C) in Chapter 1 - Chapter 1- Rational and Irrational Numbers
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Evaluate:
\frac{4-\sqrt{5}}{4+\sqrt{5}}+\frac{4+\sqrt{5}}{4-\sqrt{5}}
Answer:
\begin{array}{l} \frac{4-\sqrt{5}}{4+\sqrt{5}}+\frac{4+\sqrt{5}}{4-\sqrt{5}} \\ =\frac{4-\sqrt{5}}{4+\sqrt{5}} \times \frac{4-\sqrt{5}}{4-\sqrt{5}}+\frac{4+\sqrt{5}}{4-\sqrt{5}} \times \frac{4+\sqrt{5}}{4+\sqrt{5}} \\ =\frac{(4-\sqrt{5})^{2}}{4^{2}-(\sqrt{5})^{2}}+\frac{(4+\sqrt{5})^{2}}{4^{2}-(\sqrt{5})^{2}} \\ =\frac{16+5-8 \sqrt{5}}{16-5}+\frac{16+5+8 \sqrt{5}}{16-5} \\ =\frac{21-8 \sqrt{5}}{11}+\frac{21+8 \sqrt{5}}{11} \\ =\frac{21-8 \sqrt{5}+21+8 \sqrt{5}}{11} \\ =\frac{42}{11} \\ =3 \frac{9}{11} \end{array}
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