Question

If a=2+√3, then find the value of

$a - \times \frac{1}{a}$
please tell fast
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Answer 1

Correct Question:

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

$\huge\mathfrak{Answer:}$

Given:

• We have been given that the value of a is 2 + √3.

To Find:

• We need to find the value of a - 1/a

Solution:

As it is given that a = 2 + √3, Therefore

$\sf{ \dfrac{1}{a} = \dfrac{1}{2 + \sqrt{3} } }$

Now, we need to rationalize the denominator, so we have

$\sf{ \dfrac{1}{a} = \dfrac{1}{2 + \sqrt{3} } \times \dfrac{2 - \sqrt{3} }{2 - \sqrt{3} } }$

Using the identity :

$\sf{(x + y)(x - y) = {x}^{2} - {y}^{2} }$

We have,

$\sf \dfrac{1}{a} = \dfrac{1-\sqrt{3}}{(2)^2-(\sqrt{3})^2}$

$\implies\sf{ \dfrac{1}{a} = \dfrac{2 - \sqrt{3} }{4 - 3} }$

$\implies\sf{ \dfrac{1}{a} = 2 - \sqrt{3} }$

Now we need to find the value of a - 1/a, we have

$\sf{a - \dfrac{1}{a} = (2 + \sqrt{3}) - (2 - \sqrt{3}) }$

$\implies\sf{a + \dfrac{1}{a} = 2 + \sqrt{3} - 2 + \sqrt{3} }$

$\implies\sf{a + \dfrac{1}{a} = \sqrt{3} + \sqrt{3} }$

$\implies\sf{a - \dfrac{1}{a} = \sqrt[2]{3} }$

Hence, the value of a - 1/a is 2√3.