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If x is =root(3)-root(2) find the value of x +1/xâ€‹

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$x = \sqrt{3} - \sqrt{2 } \\\\ x + \frac{1}{x} = \sqrt{3} - \sqrt{2 } + \frac{1}{ \sqrt{3} - \sqrt{2 } }\\\\ = \sqrt{3} - \sqrt{2 } + \frac{1}{ \sqrt{3} - \sqrt{2 } } \times \frac{ \sqrt{3} + \sqrt{2 }}{ \sqrt{3} + \sqrt{2 } } \\\\ = \sqrt{3} - \sqrt{2 } + \frac{ \sqrt{3} + \sqrt{2 }}{ 3 - 2 } \\\\ = \sqrt{3} - \sqrt{2 } + \sqrt{3} + \sqrt{2 } \\\\ = 2\sqrt{3}$

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Ravindra Pindel

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