AMC / AIME · Systems of Equations · AIME / USAJMO / AMO

Systems of Equations: (Proof track.) Give a complete justification. Solve math; find math.

Linear and nonlinear systems.

Try the problem

**(Proof track.)** Give a complete justification. Solve x+y+z=6,xy+yz+zx=11,xyz=6x+y+z=6,xy+yz+zx=11,xyz=6; find x2+y2+z2x^2+y^2+z^2.

Hint and answer

Concept to use

Contest systems.

Hint

Look for a symmetric identity before solving more variables than necessary.

Answer

14

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