A binary operation * is defined on the set of real number, R, by xy = 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 + \(\sqrt{6}\)

Correct answer is D

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 + \(\sqrt{6}\)

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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 (\(\sqrt{3}\))*(\(\sqrt{2}\)) \({\color{red}2x} \times 3\)