Question

if a= 2 + √3 then the value of 1/a is
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Answer 1

EXPLANATION.

⇒ a = 2 + √3.

As we know that,

We can write equation as,

⇒ 1/a = 1/(2 + √3).

Rationalize the equation, we get.

⇒ 1/a = 1/(2 + √3) x (2 - √3)/(2 - √3).

⇒ 1/a = (2 - √3)/[(2 + √3)(2 - √3)].

⇒ 1/a = (2 - √3)/[(2)² - (√3)²].

⇒ 1/a = (2 - √3)/[4 - 3].

⇒ 1/a = (2 - √3)/1.

⇒ 1/a = 2 - √3.

Answer 2

Given :

• a= 2+√3

To Find :

The value of 1/a

Solution :

given, a = 2+√3

$\large \tt{ hence \: \frac{1}{a} = \frac{1}{2 + \sqrt{3} } }$

but, This looks odd, so we will multiply it with its Rationalising Factor (RF) to make its denominator Rational number.

$\large \tt{The \: RF \: of \: \frac{1}{2 + \sqrt{3} } \: is \: \frac{2 - \sqrt{3} }{2 - \sqrt{3} } }$

Hence, we have to multiply :

$\large \tt{ \implies \frac{1}{2 + \sqrt{3} } = \frac{1}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } }$

$\large\tt{ \implies \frac{1}{2 + \sqrt{3} } = \frac{1(2 - \sqrt{3}) }{(2 + \sqrt{3} ) (2 - \sqrt{3})} }$

$\tt{ now \: using \: the \: identity : }$

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

$\tt{we \: get \: that : }$

$\large\tt{ \implies \frac{1}{2 + \sqrt{3} } = \frac{2 - \sqrt{3} }{ {(2)}^{2} - {( \sqrt{3}) }^{2} } }$

$\large\tt{ \implies \frac{1}{2 + \sqrt{3} } = \frac{2 - \sqrt{3} }{4 - 3}}$

$\large \tt{ \implies \frac{1}{2 + \sqrt{3} } = \frac{2 - \sqrt{3} }{1}}$

$\red{ \underline{ \boxed{ \tt{ \therefore \: \frac{1}{a } = 2 - \sqrt{3} }}}}$

Hence, 1/a = 2-√3