CBSE

MATHEMATICS · Multi-part · CBSE · Mathematics · Real Numbers · Real Numbers

Problem

Let

E=\displaystyle\frac{3\sqrt{5}+2}{6-\sqrt{5}}+\frac{4\sqrt{5}-1}{5+\sqrt{5}}

. (i) Rationalise each denominator separately and simplify each fraction. (ii) Combine the simplified fractions to obtain

E

in the form

a+b\sqrt{5}

, where

a

and

b

are rational numbers. (iii) Determine the numerical values of

a

and

b

. Comment on whether

E

is rational or irrational.