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1 x^2+x-1=0 x^2+x=1 x^2=1-x 2x^3=2x×x^2=2x(1-x)=2x-2x^2 2x^3+3x^2-x=2x-2x^2+3x^2-x=x^2+x=1
2 m^2+m-1=0 m^2+m=1 m^2=1-m m^3=m×m^2=m(1-m)=m-m^2 m^3+2m^2-2008=m-m^2+2m^2+2008=m^2+m+2008 =1+2008=2009
3 3x^3-x=1 3x^3=1+x 9x^4=3x×3x^3=3x(1+x)= 3x+3x^2
9x^4+12x^3-3x^2-7x+2001=3x+3x^2+12x^3-3x^2-7x+2001=12x^3-4x+2001=4(3x^3-x)+2001=4+2001=2005
4 a-b=3(1) b+c=-5(2) (1)+(2) a+c=-2 ac-bc+a^2-ab=c(a-b)+a(a-b)=(c+a)(a-b)=-2×3=-6
5 x-1/x=3 x^2-1=3x x^2-3x=1 x^2=3x+1 x^3=x×x^2=x(3x+1)=3x^2+x
x^3-x^2-7x+5=3x^2+x-x^2-7x+5= 2x^2-6x+5=2(x^2-3x)+5=2+5=7
2 m^2+m-1=0 m^2+m=1 m^2=1-m m^3=m×m^2=m(1-m)=m-m^2 m^3+2m^2-2008=m-m^2+2m^2+2008=m^2+m+2008 =1+2008=2009
3 3x^3-x=1 3x^3=1+x 9x^4=3x×3x^3=3x(1+x)= 3x+3x^2
9x^4+12x^3-3x^2-7x+2001=3x+3x^2+12x^3-3x^2-7x+2001=12x^3-4x+2001=4(3x^3-x)+2001=4+2001=2005
4 a-b=3(1) b+c=-5(2) (1)+(2) a+c=-2 ac-bc+a^2-ab=c(a-b)+a(a-b)=(c+a)(a-b)=-2×3=-6
5 x-1/x=3 x^2-1=3x x^2-3x=1 x^2=3x+1 x^3=x×x^2=x(3x+1)=3x^2+x
x^3-x^2-7x+5=3x^2+x-x^2-7x+5= 2x^2-6x+5=2(x^2-3x)+5=2+5=7
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