Question

if 1/x = 2-√3, then x = ?​

Answer 1

1/x = 2 - √3

Rationalising the denominator:-

x = 1/2 - √3 = 1/2 -√3 * 2 + √3/2 + √3

=> 2 + √3/ 4 - 3 = 2 + √3 (Answer)

Answer 2

Given data,

$\frac{1}{x} =2-\sqrt{3}$

Here we have to find the value of $x$.

From the given equation, $x$ can be written as,

$x=\frac{1}{2-\sqrt{3} }$

Multiply and divide with $2+\sqrt{3}$

we get,

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

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

Here in denominator, they are in the form of $(a+b)(a-b)$

Formula for this is,

$(a+b)(a-b)=a^{2} -b^{2}$

Here,

$a=2;b=\sqrt{3}$

Substitute these values in formula we get,

$2^{2} -\sqrt{3} ^{2}$

$4-3$

$1$

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

Substitute $(2-\sqrt{3})(2+\sqrt{3} )}=1$ in equation one.

We get,

$x=2+\sqrt{3}$