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Real System Resolution (Posted on 2015-05-17) Difficulty: 3 of 5
Find all real solutions to this system of equations:

x5 = y + y5
y5 = z + z5
z5 = t + t5
t5 = x+ x5

No Solution Yet Submitted by K Sengupta    
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Possible Solution (Spoiler) | Comment 1 of 2
x5 = y + y5 = y(1 + y4), and since 1 + y4 is always positive

it follows that x and y cannot have opposite signs.
Using the other three equations similarly, it follows that
x, y, z and t must all have the same signs or all be zero.

Adding the four equations gives x + y + z + t = 0, so they
cannot all have the same signs, and so must all be zero:
x = y = z = 0.

Have I missed something?

  Posted by Harry on 2015-05-17 16:45:46
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