Question

If a = 2 plus root 3 then find a minus 1 by a

Answer 1

Step-by-step explanation:

$a = 2 + \sqrt{3} \\ now \frac{a - 1}{a} \\ = \frac{2 + \sqrt{3} - 1 }{2 + \sqrt{3} } \\ = \frac{1 + \sqrt{3} }{2 + \sqrt{3} } \\ = \frac{(1 + \sqrt{3})(2 - \sqrt{3} )}{(2 + \sqrt{3})(2 - \sqrt{3}) } \\ = \frac{2 + 2 \sqrt{3 } - \sqrt{3} - 3}{4 - 3} \\ = \sqrt{3} - 1$

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Answer 2

Answer:

a=2+√3

1/a=1/(2+√3)

Rationalising the denominator,

(2-√3)/(2+√3)(2-√3)

⇒ 2-√3

a-1/a=2+√3-(2-√3)

       =2+√3-2+√3=2√3

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