perplexus.info :: Just Math : Linear and Quadratic Puzzle

Linear and Quadratic Puzzle (Posted on 2015-06-18)

Determine all possible integers x, y and z such that:
x² + y² + z² = 2(yz + 1) and:
x + y + z = 4018

No Solution Yet Submitted by K Sengupta

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re: Solution / Generalization

Comment 2 of 2 |

(In reply to Solution by Jer)

The relation of the solutions to the constant 4018 is not a coincidence:

Replace 4018 with 2C.

Proceeding as before the circle becomes

(y-C)^2 + (Z-C)^2 = 1

And the (x,y,z) system has solutions

(1,C-1,C)

(1,C,C-1)

(-1,C+1,C)

(-1,C,C+1)

Posted by Jer on 2015-06-19 07:09:09

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