Given that x?y = (x + y)(x - y) + (y - x)(y + x) + xy and we need to find the value of \(\sqrt{12}?\sqrt{3}\)

x?y = (x + y)(x - y) + (y - x)(y + x) + xy = \(x^2\) - \(y^2\) + \(y^2\) - \(x^2\) + xy ( as (a-b)*(a+b) = \(a^2 - b^2\) )
= \(x^2 - x^2 - y^2 + y^2\) + xy = xy

To find \(\sqrt{12}?\sqrt{3}\) we need to compare what is before and after ? in \(\sqrt{12}?\sqrt{3}\) and x?y

=> We get to substitute x with \(\sqrt{12}\) and y with \(\sqrt{12}\) in x?y = xy to get the value of \(\sqrt{12}?\sqrt{3}\)

=> \(\sqrt{12}?\sqrt{3}\) = \(\sqrt{12} * \sqrt{3}\) = \(\sqrt{12*3}\) = \(\sqrt{36}\) = 6

So, Answer will be A
Hope it helps!

Watch the following video to learn the Basics of Functions and Custom Characters