Question

If a= 2-√3 then the value of 1/a is

Answer 1

answer is -1.232

1÷2 is 0.5

0.5-√3 is equal to -1.232

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Answer 2

Given:-

$\bullet\: \sf a = 2-\sqrt{3}$

Solution:-

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

Now, rationalize the denominator.

• To rationalize the denominator,

• multiply and divide the fraction with the conjugate of the denominator.

$\\:\implies\sf \dfrac{1}{2-\sqrt{3} } \times\dfrac{2+\sqrt{3} }{2+\sqrt{3} }$

By using the following identity:-

$\\\leadsto\underline{\boxed{\sf a^{2} -b^{2}=(a+b)(a-b) }}\bigstar$

$\\:\implies\sf \dfrac{2+\sqrt{3} }{(2)^{2} -(\sqrt{3} )^{2} }$

$\\:\implies\sf \dfrac{2+\sqrt{3} }{4-3}$

$\\:\implies\boxed{\sf 2+\sqrt{3}}\bigstar$

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