If $(x + y)^{2} = 81$ and $xy = 18$, find $x^{2} + y^{2}$.

If $(x + y)^{2} = 81$ and $xy = 18$, find $x^{2} + y^{2}$.
  1. $45$
  2. $63$
  3. $99$
  4. $117$

Solution

$(x+y)^{2} = x^{2} + y^{2} + 2xy \Rightarrow 81 = x^{2} + y^{2} + 36 \Rightarrow x^{2} + y^{2} = 45$.

Asked in: IMO

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