If $(x + y)^{2} = 49$ and $x^{2} + y^{2} = 25$, find $xy$.

If $(x + y)^{2} = 49$ and $x^{2} + y^{2} = 25$, find $xy$.
  1. $12$
  2. $24$
  3. $6$
  4. $49$

Solution

$(x + y)^{2} = x^{2} + y^{2} + 2xy \Rightarrow 49 = 25 + 2xy \Rightarrow xy = 12$.

Asked in: IMO

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