# Thread: Urgent help required !

1. ## Urgent help required !

Dear Sir ,
I felt difficulty in solving the following problems .So please help me to solve these questions . I will be very thankful to you .\

The question is in the attachment .

2. ## Re: Urgent help required !

Hello, rsaravanan!

Here is the first one . . .

$\text{1) If }\,a \:=\:7-4\sqrt{3},\;\text{ find: }\,\sqrt{a} + \frac{1}{\sqrt{a}}$

$\text{Note that: }\:a \;=\;7 - 4\sqrt{3} \;=\; (2-\sqrt{3})^2$

$\text{Hence: }\:\sqrt{a} \;=\;\sqrt{(2-\sqrt{3})^2} \;=\;2-\sqrt{3}$

$\text{Then: }\:\sqrt{a} + \frac{1}{\sqrt{a}} \;=\;\left(2-\sqrt{3}\right) + \frac{1}{2-\sqrt{3}}$

$\text{Rationalize: }\:\left(2-\sqrt{3}\right)\;+\; \frac{1}{2-\sqrt{3}}\!\cdot\!{\color{blue}\frac{2+\sqrt{3}}{2 +\sqrt{3}}} \;\;=\;\;\left(2-\sqrt{3}\right)\;+\;\frac{2+\sqrt{3}}{4-3}$

. . . . . . . . . . $=\;\;\left(2 - \sqrt{3}\right) + \left(2 + \sqrt{3}\right) \;\;=\;\;\boxed{4}$

3. ## Re: Urgent help required !

Thank you very much sir

4. ## Re: Urgent help required !

In the second problem, all three terms should be cubed. Also, just a heads up, I solved it on another forum on which these questions were posted.