Difference between revisions of "2017 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 5"
(Created page with " == Problem == Find all real triples <math>(x,y,z)</math> which are solutions to the system: <math>x^3 + x^2y + x^2z = 40</math> <math>y^3 + y^2x + y^2z = 90</math> <math...") |
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== Solution== | == Solution== | ||
| − | + | There are <math>3</math> solutions <math>(2,3,5)</math> or <math>(-\sqrt[3]{\frac{40}{3}} ,\sqrt[3]{45},\sqrt[3]{\frac{5^4}{3}})</math> or <math>(\sqrt[3]{20},-\frac{3\sqrt[3]{20}}{ 2} , \frac{5\sqrt[3]{20}}{ 2})</math> | |
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== See also == | == See also == | ||
which are solutions to the system:
solutions 
or ![$(-\sqrt[3]{\frac{40}{3}} ,\sqrt[3]{45},\sqrt[3]{\frac{5^4}{3}})$](http://latex.artofproblemsolving.com/9/0/5/905c22232f5bb60b529c2241abffe49a9380efcd.png)
or ![$(\sqrt[3]{20},-\frac{3\sqrt[3]{20}}{ 2} , \frac{5\sqrt[3]{20}}{ 2})$](http://latex.artofproblemsolving.com/1/f/5/1f5ffbd968f934c954cd5346a24ca580d95a47ec.png)
