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A Real Solution Puzzle (Posted on 2006-07-30) Difficulty: 3 of 5
Find all real solutions x, y, z of the following system of equations:

x³ + y = 12x + 20
2y³ + z = 24y + 36
3z³ + x = 36z + 52

See The Solution Submitted by K Sengupta    
Rating: 3.0000 (2 votes)

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Some Thoughts An easy one Comment 5 of 5 |
Seeing the regularity in the equations, and the difference (16) between 20 and 36, and 36 and 52, led me to think about powers of 2, and quickly got x=y=z=4 as an answer.

Then, I decided to write y as a function of x as per the first equation; substitute in the second, and write z as a function of x, and finally substitute in the third, that became an enormous polynomial in x... which I didn't want to solve!

  Posted by Federico Kereki on 2006-07-30 16:27:10
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