Question

Find the value of the expression using suitable identities:$\frac{2+1}{2\times 2\times 2+1\times 1\times 1}$ (2 marks)

Answer 1

On taking a = 2 and b = 1, the given expression becomes

$\frac{a+b}{a^3+b^3}$
= $\frac{a+b}{(a+b)(a^2-ab+b^2)}$ (1 mark)
= $\frac{1}{(a^2-ab+b^2)}$
= $\frac{1}{(2^2-2\times 1+1^2)}$
=$\frac{1}{(4-2+1)}$
=$\frac{1}{3}$ (1 mark)