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If x = \(\frac{\sqrt{3}+{\sqrt2}}{\sqrt{3}-{\sqrt2}}\) and y = \(\frac{\sqrt{3}-{\sqrt2}}{\sqrt{3}+{\sqrt2}}\) then the value of x + y x = (√3+√2)/(√3-√2) and y = (√3-√2)/(√3+√2) A) 5 B) 5 + 2√6 C) 10 D) 5 – 2√6 |
Answer» Correct option is (C) 10 x+y \(=\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}+\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}\) \(=\frac{(\sqrt{3}+\sqrt{2})^2+(\sqrt{3}-\sqrt{2})^2}{(\sqrt{3}-\sqrt{2})(\sqrt{3}+\sqrt{2})}\) \(=\frac{(3+2+2\sqrt6)+(3+2-2\sqrt6)}{3-2}\) \(=\frac{5+5}1=10\) Correct option is C) 10 |
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