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# For all numbers x and y, the operation ? is defined by x?y = (x + y)(x

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For all numbers x and y, the operation ? is defined by x?y = (x + y)(x [#permalink]
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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