A binary operation * is defined on the set of real number, R, by x*y = x\(^2\) – y\(^2\) + xy, where x, \(\in\) R. Evaluate (\(\sqrt{3}\))*(\(\sqrt{2}\))
\({\color{red}2x} \times 3\)
- 1 - \(\sqrt{6}\)
- \(\sqrt{6}\) - 1
- \(\sqrt{6}\)
-
1 + \(\sqrt{6}\)
The correct answer is: D
Explanation
x*y = x\(^2\) - y\(^2\) + xy
(\(\sqrt{3}\))*(\(\sqrt{2}\)) = (\(\sqrt{3}\))\(^2\) - (\(\sqrt{2}\))\(^2\) + \(\sqrt{3}\) x \(\sqrt{2}\)
= 3 - 2 + \(\sqrt{6}\)
= 1 + \(\sqrt{6}\)