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Real Value Validation (Posted on 2015-02-01) Difficulty: 3 of 5
Each of X, Y and Z is a real number that satisfies both of these equations:
X + Y = 2, and:
X*Y - Z2 = 1

Find the value of X5 + Y5 + Z5

No Solution Yet Submitted by K Sengupta    
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Some Thoughts re: Quick and dirty (spoiler) | Comment 2 of 3 |
(In reply to Quick and dirty (spoiler) by Steve Herman)

Yes.

Alternatively: x(2-x)-1 =z^2; -(x-1)^2 = z^2, and z has to be 0, so x is 1. y+1=2 simplifies to y=1.

So x5 + y5 + z5= 2.



Edited on February 1, 2015, 11:34 pm
  Posted by broll on 2015-02-01 23:28:57

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