Question

x=(4+2root3)find (x-2÷root x)

Answer 1

Answer:

5 + √3

Solution:

Given : x = 4 + 2√3

To find : x - 2/√x = ?

Firstly ,

Let's find the value of √x .

We have ;

=> x = 4 + 2√3

=> x = 3 + 1 + 2√3

=> x = 3 + 2√3 + 1

=> x = (√3)² + 2•√3•1 + (1)²

=> x = (√3 + 1)²

=> √x = √3 + 1

Now,

Let's find the value of 2/√x .

We have ;

=> √x = √3 + 1

=> 1/√x = 1 / (√3 + 1)

=> 1/√x = (√3 - 1) / (√3 + 1)(√3 - 1)

=> 1/√x = (√3 - 1) / { (√3)² - 1² }

=> 1/√x = (√3 - 1) / (3 - 1)

=> 1/√x = (√3 - 1) / 2

=> 2/√x = √3 - 1

Now,

x - 2/√x = (4 + 2√3) - (√3 - 1)

= 4 + 2√3 - √3 + 1

= 5 + √3

Hence,

The required answer is :

5 + √3