-12x+8=3x^4-2x^3-9x^2+4

题目

-12x+8=3x^4-2x^3-9x^2+4

答案

高次的方程,就是需要做因式分解,从而得到求解
-12x +8 = 3(x四次方)- 2(x立方)- 9(x平方) +4
3(x四次方)- 2(x立方)- 9x" + 12x -4 = 0
3(x四次方)- 2(x立方)-[ 9x" - 2*(3x)*2 +4 ] = 0
(x立方)(3x - 2) - (3x - 2)" = 0
(3x - 2)[(x立方)- (3x - 2)] = 0
(3x - 2)[(x立方)- x" + x" - 3x + 2 ] = 0
(3x - 2)[(x立方 - x")+ (x" - 3x + 2)] = 0
(3x - 2)[ x"(x - 1) + (x - 1)(x - 2)] = 0
(3x - 2)(x - 1)[ x" + x - 2 ] = 0
(3x - 2)(x - 1)"(x + 2) = 0
这个方程的解,就是
x1 = 2/3
x2 = x3 = 1
x4 = -2