回复：Assume f(x)'s coefficients are all real;

来源: jinjing 于 2011-07-13 20:37:56 [] [旧帖] [给我悄悄话] 阅读数 : (247 bytes)
回答: Assume f(x)'s coefficients are all real; 由 乱弹 于 2011-07-13 16:56:53

The b=2,a=2/9,f(0)=8/9.

If b is not 2, f(f(x)) at least 2 roots.

f(f(x))=a(a(x-5)^2)(a(x-5)^2+2-b) or f(f(x))=a(a(x-5)^2+b-2))(a(x-5)^2).

5,5+SQUAT(b-2)/a or 5,5+SQUT(2-b) are roots. contradiction to only one root 5.

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