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 (\(\sqrt{3}\))*(\(\sqrt{2}\))
\({\color{red}2x} \times 3\)
\({\color{red}2x} \times 3\)
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Correct Answer: Option 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 + \(\sqrt{6}\)
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 + \(\sqrt{6}\)