Question

if a = 2 + √3 , find a- 1/ a

Answer 1

Hey friend !!!!!

•°• Here's your answer •°•

$= a = 2 + \sqrt{3} then \: find \: a - \frac{1}{a} \\ \\ let \: us \: find \: \frac{1}{a} \\ \\ = \frac{1}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } \\ \\ = \frac{2 - \sqrt{3} }{ {2}^{2} - { \sqrt{3} }^{2} } \\ \\ = \frac{2 - \sqrt{3} }{4 - 3} \\ \\ = \frac{2 - \sqrt{3} }{1} \\ \\ = 2 - \sqrt{3} \\ \\ now \: (a - \frac{1}{a} ) \\ \\ = 2 + \sqrt{3 } - ( \: 2 - \sqrt{3} ) \\ \\ = 2 + \sqrt{3} - 2 + \sqrt{3} \\ \\ = \sqrt{3} + \sqrt{3} \\ \\ = 2 \sqrt{3}$

Identity used
( a + b ) ( a - b ) = a^2 - b^2

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