Question

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Answer 1

Question :-

If x = 7 + 4√3, then find the value of √x + 1/√x ?

Given :-

$\purple\implies \sf \: x = 7 + \sqrt[4]{3}$

To find :-

$\purple \implies \sf \sqrt{x} + \frac{1}{ \sqrt{x} }$

On substituting the value of x, We get

$\purple \implies \sf \sqrt{7 + \sqrt[4]{3} } + \sf\frac{1}{ \sqrt{7 + \sqrt[4]{3} } }$

Factor the expressions...

$\sf \pink{\boxed{\boxed{\sqrt{(2 + \sqrt{ {3)}^{2} } } + \frac{1}{ \sqrt{(2 + \sqrt{3) {}^{2} } }}}}}$

Simplify the roots...

$\sf \implies \boxed{2 + \sqrt{3} + \frac{1}{2 + \sqrt{3} }}$

Rationalize...

$\sf \implies \boxed{ 2 + \sqrt{3} + 2 - \sqrt{3}}$

Eliminate the opposites...

$\sf \implies \: 2 + 2$

Calculate the sum...

$\implies \sf \red{\boxed{\boxed{4}}}$