Answer for the question given in the picture

1.	Answer for the question given in the picture
Answer» QUESTION : If a = 2 + √3,then find the VALUE of a - 1/a SOLUTION : GIVEN that a = 2 + √3 Here, $\sf \: \dfrac{1}{a} = \dfrac{1}{2 + \sqrt{3} } \\ \\ \longmapsto \: \sf \: \dfrac{1}{a} = \dfrac{1}{2 + \sqrt{3} } \times \dfrac{2 - \sqrt{3} }{2 - \sqrt{3} } \\ \\ \longmapsto \: \sf \: \dfrac{1}{a} = \dfrac{2 - \sqrt{3} }{ {2}^{2} - ( \sqrt{3}) {}^{2} } \\ \\ \longmapsto \: \boxed{\sf \: \dfrac{1}{a} = 2 - \sqrt{ 3} }$ Now, $\sf \: a - \dfrac{1}{a} \\ \\ = \sf \: (2 + \sqrt{3} ) - (2 - \sqrt{3} ) \\ \\ = \sf \: 2 \sqrt{3}$

Answer»

QUESTION :

If a = 2 + √3,then find the VALUE of a - 1/a

$\sf \: \dfrac{1}{a} = \dfrac{1}{2 + \sqrt{3} } \\ \\ \longmapsto \: \sf \: \dfrac{1}{a} = \dfrac{1}{2 + \sqrt{3} } \times \dfrac{2 - \sqrt{3} }{2 - \sqrt{3} } \\ \\ \longmapsto \: \sf \: \dfrac{1}{a} = \dfrac{2 - \sqrt{3} }{ {2}^{2} - ( \sqrt{3}) {}^{2} } \\ \\ \longmapsto \: \boxed{\sf \: \dfrac{1}{a} = 2 - \sqrt{ 3} }$