方程x3-3x2+4=
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方程x3-3x2+4=方程x3-3x2+4=方程x3-3x2+4=∵x³-3x²+4=x³+x²-4(x²-1)=x²(x+1)-4(x+1
方程x3-3x2+4=
方程x3-3x2+4=
方程x3-3x2+4=
∵x³-3x²+4
=x³+x²-4(x²-1)
=x²(x+1)-4(x+1)(x-1)
=(x+1)(x²-4x+4)
=(x+1)(x-2)²=0
∴x=-1或2
x^3-2=(x-3的根号下2)(x^2+x3的根号下2+x3的根号下4)=0
x=3的根号下2
x3-3x2+4=x^3+1-3x^2+3=(x+1)(x^2-x+1)-3(x-1)(x+1)=
=(x+1)(x^2-4x+4)=(x+1)(x-2)^2=0
x1=-1,x2=2,x3=2
考察因式分解,
x^3-3x^2+4=(x^3+x^2)-(4x^2+4)=(x+1)x^2-4(x^2-1)=(x+1)x^2-4(x+1)(x-1)
=(x+1)[x^2-4(x-1)]=(x+1)(x-2)^2,
故方程的解为 x=-1,或 x=2(重根)。
X^3+1-3X^2+3=0
(X+1)(X^2-X+1)-3(X^2-1)=0
(X+1)(X^2-X+1)-3(X-1)(X+1)=0
(X+1)(X^2-X+1-3X+3)=0
(X+1)(X^2-4X+4)=0
(X+1)(X-2)^2=0
所以X=-1或X=2
方程x3-3x2+4=
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