1.

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

Answer»

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.


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