Question

If x =root5+root4then find the value of x+1/x

Answer 1

Answer:

Step-by-step explanation:

We will solve the question by

RATIONALISATION:-

In this we multiply the numerator and denominator by the inverse of the sign of the denominator.

So we need to find x+ 1/x.

First we will rationalise 1/x

$\frac{1}{\sqrt{5}+\sqrt{4} } * \frac{\sqrt{5}-\sqrt{4} }{\sqrt{5}-\sqrt{4}}$

$= \frac{\sqrt{5}-\sqrt{4}}{(\sqrt{5}+\sqrt{4})(\sqrt{5}-\sqrt{4})}$

Using identity (a^2-b^2) in denominator,

$\frac{\sqrt{5}-\sqrt{4}}{(\sqrt{5}) ^{2}-(\sqrt{4}) ^{2} }$

$\frac{\sqrt{5}-\sqrt{4}}{5-4} \implies \sqrt{5}-\sqrt{4}$

Now placing the values of x and rationalised 1/x,

$\sqrt{5}+\sqrt{4}+\sqrt{5}-\sqrt{4}\\\implies 2\sqrt{5}$

So $2\sqrt{5}$ is the answer.