If $(x^{2} - y^{2}) = 18$ and $(x - y) = 3$ , find the value of $x^{2} + y^{2} + 2 x y$ .

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243

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Solution

The correct option is C
243

$(x^{2} - y^{2}) = (x - y) (x + y) = 18$

$(x - y) = 3$
$(x + y) = \frac{18}{3} = 6$

We know the following is an identity

$(x^{2} + y^{2} + 2 x y) = (x + y)^{2} = 6^{2} = 36$

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