Question

if x =2-√3, then find the value of x-1/x​

Answer 1

Step-by-step explanation:

Given,

$x = 2 - \sqrt{3}$

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

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

$\frac{1}{x} = \frac{2 - \sqrt{3} }{4 - 3}$

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

Now,

$x - \frac{1}{x}$

$= 2 + \sqrt{3} - 2 - \sqrt{3}$

$= 2 + 2$

$= 4$

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Answer 2

ANSWER:-

$2 \sqrt{3}$

SOLUTION:-

x→2-√3 (Given)

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

Now,

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

Hence, our answer is 2√3.

Hope You Understood.