Question

If a = 2 + √3 ,then find the value of (a - 1/a) ,
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Answer 1

Answer:

(a - 1/a)= 2 + √3 - 1/ 2 + √3

(2+√3)²-1 / 2+√3

6+4√3/ 2 + √3

Answer 2

GIVEN :-

• a = 2 + √3 .

TO FIND :-

• The value of a - 1/a.

SOLUTION :-

$\\ : \implies \displaystyle \sf \bigg( \: a - \frac{1}{a} \bigg) = 2 + \sqrt{3} - \frac{1}{2 + \sqrt{3} }$

${ \displaystyle \sf \: \dag \: Rationalise \: the \: denominator.}$

$: \implies \displaystyle \sf \bigg( \: a - \frac{1}{a} \bigg) = 2 + \sqrt{3} - \frac{1(2 - \sqrt{3} )}{(2 + \sqrt{3}) (2 - \sqrt{3} )}$

$: \implies \displaystyle \sf \bigg( \: a - \frac{1}{a} \bigg) = 2 + \sqrt{3} - \frac{2 - \sqrt{3} }{(2) ^{2} - ( \sqrt{3} ) ^{2} }$

$: \implies \displaystyle \sf \bigg( \: a - \frac{1}{a} \bigg) = 2 + \sqrt{3} - \frac{2 - \sqrt{3} }{4 - \sqrt{9} }$

$: \implies \displaystyle \sf \bigg( \: a - \frac{1}{a} \bigg) = 2 + \sqrt{3} - \frac{2 - \sqrt{3} }{4 - 3}$

$: \implies \displaystyle \sf \bigg( \: a - \frac{1}{a} \bigg) = 2 + \sqrt{3} - \frac{2 - \sqrt{3} }{1}$

$: \implies \displaystyle \sf \bigg( \: a - \frac{1}{a} \bigg) = 2 + \sqrt{3} - (2 - \sqrt{3})$

$: \implies \displaystyle \sf \bigg( \: a - \frac{1}{a} \bigg) = 2 - 2 + \sqrt{3} + \sqrt{3}$

$: \implies \displaystyle \sf \bigg( \: a - \frac{1}{a} \bigg) = 0 + 2 \sqrt{3}$

$: \implies \underline{ \bold{ \boxed{ \displaystyle \mathfrak{ \bigg( \: a - \frac{1}{a} \bigg) = 2 \sqrt{3}}}}}$