作业帮x^4-5x^2+10x-6怎么解?
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/15 14:09:24
x^4-5x^2+10x-6怎么解?
x^4 - 5x^2 + 10x - 6
= x^4 - x^2 - ( 4x^2 - 4x ) + 6x - 6
= x^2 ( x^2 - 1 ) - 4x ( x - 1 ) + 6 ( x -1 )
= x^2 ( x + 1 ) ( x - 1 ) - 4x ( x - 1 ) + 6 ( x - 1 )
= (x-1) [ x^2 ( x + 1 ) - 4x + 6 )
= (x-1) ( x^3 + x^2 - 4x + 6 )
= (x-1) ( x^3 + 8 + x^2 - 2x + 4 - 2x - 6 )
= (x-1) [ (x+2)(x^2 - 2x + 4) + x^2 - 2x + 4 - 2x - 6 )
= (x-1) [ (x+3)(x^2 - 2x + 4) - 2 (x+3) ]
= (x-1) [ (x+3)(x^2 - 2x + 2) ]
x^2 - 2x + 2 = (x-1)^2 + 1 > 0
所以 x^4 - 5x^2 + 10x - 6 = 0 的解是 x = 1 或 x = -3
这个应该是对的啦～
= x^4 - x^2 - ( 4x^2 - 4x ) + 6x - 6
= x^2 ( x^2 - 1 ) - 4x ( x - 1 ) + 6 ( x -1 )
= x^2 ( x + 1 ) ( x - 1 ) - 4x ( x - 1 ) + 6 ( x - 1 )
= (x-1) [ x^2 ( x + 1 ) - 4x + 6 )
= (x-1) ( x^3 + x^2 - 4x + 6 )
= (x-1) ( x^3 + 8 + x^2 - 2x + 4 - 2x - 6 )
= (x-1) [ (x+2)(x^2 - 2x + 4) + x^2 - 2x + 4 - 2x - 6 )
= (x-1) [ (x+3)(x^2 - 2x + 4) - 2 (x+3) ]
= (x-1) [ (x+3)(x^2 - 2x + 2) ]
x^2 - 2x + 2 = (x-1)^2 + 1 > 0
所以 x^4 - 5x^2 + 10x - 6 = 0 的解是 x = 1 或 x = -3
这个应该是对的啦～
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