Question

If x=7+4 root 3 find the value of (x root +1/x root) ​

Answer 1

ANSWER:-

Given:

If x= 7 + 4√3

To find:

Find the value of,

$( \sqrt{x} + \frac{1}{ \sqrt{x} } )$

Solution:

x = 7+ 4√3

=) x = 4+3 + 2×2× √3

=) x= (√4)² + (√3)² + 2× 2 ×√3

=) x = (2)² + (√3)² + 2× 2 ×√3 [In (a+b)²]

=) x = (2 + √3)²

=) √x = 2+√3

Now,

Putting the value in √x + 1/√x we have;

By rationalizing method;

$= > \frac{1}{ \sqrt{x} } = \frac{1}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } \\ \\ = > \frac{2 - \sqrt{3} }{ {2}^{2} - 3 } \\ \\ = > \frac{2 - \sqrt{3} }{4 - 3} \\ \\ = > \frac{2 - \sqrt{3} }{1} = > 2 - \sqrt{3}$

Therefore,

√x + 1/√x

=) 2+ √3+ 2 -√3

=) 2+ 2

=) 4. [answer]

Hence,

4 is the required value.

Hope it helps ☺️

Answer 2

Answer:

Thank you for the question and answer

Step-by-step explanation: