If $(x+y) = 5$ and $(x-y) = 3$, find $x^{2} + y^{2}$.

If $(x+y) = 5$ and $(x-y) = 3$, find $x^{2} + y^{2}$.
  1. $17$
  2. $15$
  3. $25$
  4. $8$

Solution

$x^{2} + y^{2} = \dfrac{(x+y)^{2} + (x-y)^{2}}{2} = \dfrac{25 + 9}{2} = 17$.

Asked in: IMO

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