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| Real System Resolution (Posted on 2015-05-17) |
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Find all real solutions to this system of equations:
x5 = y + y5
y5 = z + z5
z5 = t + t5
t5 = x+ x5
Possible Solution (Spoiler)
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 | Comment 1 of 2
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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?
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Posted by Harry
on 2015-05-17 16:45:46 |
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