WAEC 2020 · Paper 1 · Q1

Binary operations

A binary operation $*$ is defined on the set of real numbers, $\mathbb{R}$ , by $x * y = x^2 - y^2 + xy$ , where $x, y \in \mathbb{R}$ . Evaluate $(\sqrt{3}) * (\sqrt{2})$ .

Worked solution (try it first)

Put $x = \sqrt{3}$ and $y = \sqrt{2}$ into the rule.
The squares are $x^2 = 3$ and $y^2 = 2$ .
The product is $xy = \sqrt{3} \times \sqrt{2} = \sqrt{6}$ .
So $(\sqrt{3}) * (\sqrt{2}) = 3 - 2 + \sqrt{6}$
$= 1 + \sqrt{6}$ , option D.

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