Question

If x=1/√3+2,then[x+1/x]^2=​

Answer 1

Answer: [x +1/x}^2 will be 16

Step-by-step explanation:

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

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

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

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

x+1/x=4

So, [x +1/x}^2 will be 16

Answer 2

Answer:

16

Solution:

Given : x = 1/(√3 - 2)

To find : (x + 1/x)² = ?

We have ;

=> x = 1/(√3 - 2)

On rationalising the denominator of the term in RHS , we have ;

=> x = (√3 + 2) / (√3 - 2)(√3 + 2)

=> x = (√3 + 2) / [ (√3)² - 2² ]

=> x = (√3 + 2) / (3 - 4)

=> x = (√3 + 2) / (-1)

=> x = - (√3 + 2)

=> x = -√3 - 2

Also,

If x = 1/(√3 - 2) , then

1/x = √3 - 2

Now,

[ x + 1/x ]² = [ -√3 - 2 + √3 - 2 ]²

= [ - 4 ]²

= 16

Hence,

The required answer is 16 .