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SMO 2009 Junior Round 1 Question 8

SMO · SMO 2009 Junior Round 1

Question 8

Given real numbers $x,y$ with $x+xy+y=2+3\sqrt2$ and $x^2+y^2=6$, find $|x+y+1|$.
  1. $1+\sqrt3$
  2. $2-\sqrt3$
  3. $2+\sqrt3$
  4. $3-\sqrt2$
  5. $3+\sqrt2$