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Yes. y = x6 has only one solution, at (0, 0).

In fact, if you think about it, the family of equations y = a(x+b)6 (where a and b can be any real constant; including x6, 2(x-4)6, 42(x+1)6, and so on) all have one solution. Other than these equations, however, sixth-degree polynomials almost always have multiple solutions or none at all.

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Q: Is it possible for a sixth-degree polynomial to have only one solution?
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