Question

a=2+✓3 find the value of a-1/a​

Answer 1

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a - 1/a = 1

• As cancelling both a by a. . .

Answer 2

Answer:

a - 1/a = 0

Step-by-step explanation:

If

$a = 2 + \sqrt{3}$

Then,

$\frac{1}{a} = \frac{1}{2 + \sqrt{3} }$

Rationaise the denominator,

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

$= \frac{2 - \sqrt{3} }{ {(2)}^{2} - {( \sqrt{3} )}^{2} }$

Since, (a + b)(a - b) = a^2 - b^2

$= \frac{2 - \sqrt{3} }{4 - 3}$

$= 2 - \sqrt{3}$

Therefore,

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

Solving further,

$= 2 - \sqrt{3} - 2 + \sqrt{3}$

$= 0$