olymmath

HMMT 2006 A2

  • Algebra
  • Answer

Find all real solutions (x,y)(x, y) of the system x2+y=12=y2+xx^{2}+y=12=y^{2}+x.

Dataset text NuminaMath olympiads. Quoted with source.

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(3,3),(-4,-4),\left(\frac{1+3 \sqrt{5}}{2}, \frac{1-3 \sqrt{5}}{2}\right),\left(\frac{1-3 \sqrt{5}}{2}, \frac{1+3 \sqrt{5}}{2}\right)

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