(X-1)/2=cos(2π/9)

x0=0, x1=1, x2=X

x3=X(x2-x1)+x0=X^2-X

x4=X(x3-x2)+x1=X^3-2X^2+1　

x5=X(x4-x3)+x2=X^4-3X^3+X^2+2X=X^2-X

x6=X, x7=1

x8=0, x9= 0

Σxi=X^3+3　

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X=1+2cos(2π/9)

3(2x^4-5x^3+6x^2-3x+3)/(X^3+3)^2=1/(2cos(π/9))^2

半角公式を使えばいったん次数は下がると思われる

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3(2x^4-5x^3+6x^2-3x+3)/(X^3+3)^2=1/2(1+cos(2π/7))

3(2x^4-5x^3+6x^2-3x+3)/(X^3+3)^2=1/2(1+(X-1)/2)

3(2x^4-5x^3+6x^2-3x+3)/(X^3+3)^2=1/(1+X)

3(x+1)(2x^4-5x^3+6x^2-3x+3)=(X^3+3)^2

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　　ｃｏｓ（3θ）＝ｃｏｓ（6θ）

32x^6-48x^4+18x^2-1=4x^3-3x

32x^6-48x^4-4x^3+18x^2+3x-1=0

y^6/2-3y^4-y^3/2+9y^2/2+3y/2-1=0

y^6-6y^4-y^3+9y^2+3y-2=0

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x=y+1

(y+2)f(y)=((y+1)^3+3)^2=(y^3+3y^2+3y+4)^2=y^6+9y^4+9y^2+16+6y^5+6y^4+8y^3+18y^3+24y^2+24y

(y+2)f(y)=((y+1)^3+3)^2=(y^3+3y^2+3y+4)^2=y^6+6y^5+15y^4+26y^3+33y^2+24y+16

y^6+6y^5+15y^4+26y^3+33y^2+24y+16-(y+2)f(y)＝０

これが

y^6-6y^4-y^3+9y^2+3y-2=0

に等しい。

6y^5+21y^4+27y^3+24y^2+21y+18-(y+2)f(y)＝０

(y+2)f(y)=6y^5+21y^4+27y^3+24y^2+21y+18

(y+2)(6y^4+9y^3+9y^2+6y+9)

3(y+2)(2y^4+3y^3+3y^2+2y+3)

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y=x-1

3(x+1)(2(x-1)^4+3(x-1)^3+3(x-1)^2+2(x-1)+3)

3(x+1)(2(x^4-4x^3+6x^2-4x+1)+3(x^3-3x^2+3x-1)+3(x^2-2x+1)+2(x-1)+3)

3(x+1)((2x^4-8x^3+12x^2-8x+2)+(3x^3-9x^2+9x-3)+(3x^2-6x+3)+(2x-2)+3)

3(x+1)((2x^4-5x^3+6x^2-3x+3))

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