Question

please answer ... it's urgent​

Answer 1

Answer:

4(2+root3)

Step-by-step explanation:

HOPE THIS BRING A SMILE IN YOUR FACE

Answer 2

Solution

$a\: =\: 7\: - \: 4\sqrt{3}$

Rationalisation

$\dfrac{1}{a}\: =\: \dfrac{1}{7\: - \: 4\sqrt{3}}\times\dfrac{7\: +\: 4\sqrt{3}}{7\: +\: 4\sqrt{3}}$

$\dfrac{1}{a}\: =\: \dfrac{7\: + \: 4\sqrt{3}}{(7)^{2}\:-\:(4\sqrt{3})^{2}}$

$\dfrac{1}{a}\:=\: \dfrac{7\:+\:4\sqrt{3}}{49\: - \: 48}$

$\dfrac{1}{a}\: =\: 7\: + \: 4\sqrt{3}$

$a \: =\: 7\: - \: 4\sqrt{3}$

Now,

Simplest Equation

$a\:+\:\dfrac{1}{a}\: =\: 7\:-\cancel{\:4\sqrt{3}}+7\:+\:\cancel{4\sqrt{3}}$

$a\:+\:\dfrac{1}{a}\:=\: 7\: +\: 7$

$a\:+\:\dfrac{1}{a}\:=\:14$

Taking square

$\Big(\sqrt{a}\:+\:\dfrac{1}{\sqrt{a}}\Big)^{2}\: =\: a \: +\: \dfrac{1}{a}\: +\: 2\cancel{\sqrt{a}} \times\dfrac{1}{\cancel{\sqrt{a}}}$

$\Big(\sqrt{a}\:+\:\dfrac{1}{\sqrt{a}}\Big)^{2}\: =\: a \: +\: \dfrac{1}{a}\: + \:2$

$\sqrt{a}\:+\:\dfrac{1}{\sqrt{a}}\: =\: \sqrt{(14 \:+\:2)}$

$\sqrt{a}\:+\:\dfrac{1}{\sqrt{a}}\: =\: \sqrt{16}$

Answer

$\boxed{\sqrt{a}\:+\:\dfrac{1}{\sqrt{a}}\: =\: 4}$