Question

if a=√3+2 then find value of a-1/a​

Answer 1

Step-by-step explanation:

if a=√3+2

thena-1/a

=√3+2-1/√3+2

=√3-1/√3+2

Answer 2

Hey friend here is the answer you are looking for

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

on rationalising the denominator we get :

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

using the identity

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

we get

$\frac{1}{a} = \frac{ \sqrt{3} - 2}{ { (\sqrt{3}) }^{2} - ( {2)}^{2} } \\ \frac{ \sqrt{3} - 2}{3 - 4} \\ \frac{ \sqrt{3} - 2 }{ - 1} \\ \frac{ - (2 - \sqrt{3}) }{ - 1} \: \: \: \: \: \: \:cut \: the \: subtract \: sign \\ \frac{1}{a} = 2 - \sqrt{3}$

by putting the values..

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

here is your answer...

hope it will help you..