已知x^2+3x=6,求x^3+x^2-12x+10的值

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已知x^2+3x=6,求x^3+x^2-12x+10的值

已知x^2+3x=6,求x^3+x^2-12x+10的值
已知x^2+3x=6,求x^3+x^2-12x+10的值

已知x^2+3x=6,求x^3+x^2-12x+10的值
x^2+3x=6
∴x²+3x-6=0
x³+x²-12x+10
=x³+3x²-6x-2x²-6x+12-2
=x(x²+3x-6)-2(x²+3x-6)-2
∵x²+3x-6=0
∴原式=-2

x²+3x=6
x²=-3x+6
x^3=x*x²=x(-3x+6)=-3x²+6x
所以
x^3+x²-12x+10
=-3x²+6x+x²-12x+10
=-2x²-6x+10
=-2(x²+3x)+10
=-12+10
=-2

  x^2+3x=6
  x^2=-3x+6
  x^3=x*x^2=x(-3x+6)=-3x^2+6x
  所以
  x^3+x^2-12x+10
  =-3x^2+6x+x^2-12x+10
  =-2x^2-6x+10
  =-2(x^2+3x)+10
  =-2*6+10
  =-2
  或者: x^3+x^2...

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  x^2+3x=6
  x^2=-3x+6
  x^3=x*x^2=x(-3x+6)=-3x^2+6x
  所以
  x^3+x^2-12x+10
  =-3x^2+6x+x^2-12x+10
  =-2x^2-6x+10
  =-2(x^2+3x)+10
  =-2*6+10
  =-2
  或者: x^3+x^2-12x+10
=x^3+3x^2-2x^2-6x-6x+10
=x^3+3x^2-6x-2x^2-6x+10
=x(x^2+3x-6)-2x^2-6x+10
=-2x^2-6x+10
=-2(x^2+3x-6)-12+10
=-12+10
=-2

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