Question

if x = 2 + root 3 . find the value of x - 1 /x​

Answer 1

value of x - 1/x is 2√3

see the attached photo for solution

Answer 2

$\sf{Answer}$

Step by step explanation:-

Given :-

x = 2 + √3.

To find :-

x - 1/x

Solution:-

x - 1/x =

2 + √3 - $\frac{1}{2 + √3}$

Take LCM

$\frac{ (2 + √3)²-1}{2 + √3}$

$\frac{4+3+4√3-1}{2 + √3}$

$\frac{ 6 +4√3 }{2 + √3}$

Multiply and divide with rationalizing factor of denominato

Rationalizing factor of 2 + √3 is 2- √3.

$\frac{ 6 +4√3 }{2 + √3}$ × $\frac{2- √3}{2- √3}$

4√3(2- √3) + 6 (2- √3) /1

8√3 -12 +12 -6√3. /1

2√3

So, x -1/x is 2√3.

Used identities:-

(a +b)(a-b) = a²-b²

(a +b)² = a²+b²+2ab

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