2017 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 5

Problem

Find all real triples $(x,y,z)$ which are solutions to the system:

$x^3 + x^2y + x^2z = 40$

$y^3 + y^2x + y^2z = 90$

$z^3 + z^2x + z^2y = 250$

2017 UNM-PNM Contest II (Problems • Answer Key • Resources)
Preceded by Problem 4	Followed by Problem 6
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10
All UNM-PNM Problems and Solutions