解方程6x^5-41x^4+97x^3-97x^2+41x-6=0
答案:4 悬赏:20 手机版
解决时间 2021-01-13 22:30
- 提问者网友：姑娘长的好罪过
- 2021-01-13 06:45
解方程6x^5-41x^4+97x^3-97x^2+41x-6=0
最佳答案
- 五星知识达人网友：由着我着迷
- 2021-01-13 06:52
将原等式左边分解因式得如下过程：
6x^5-41x^4+97x^3-97x^2+41x-6
= (x-1)(6x^4-35x^3+62x^2-35x+6)
= (x-1)(x-2)(6x^3-23x^2+16x-3)
= (x-1)(x-2)(x-3)(6x^2-5x+1)
= (x-1)(x-2)(x-3)(2x-1)(3x-1) = 0
故得方程所有解：x=1,x=2,x=3,x=1/2,x=1/3,
6x^5-41x^4+97x^3-97x^2+41x-6
= (x-1)(6x^4-35x^3+62x^2-35x+6)
= (x-1)(x-2)(6x^3-23x^2+16x-3)
= (x-1)(x-2)(x-3)(6x^2-5x+1)
= (x-1)(x-2)(x-3)(2x-1)(3x-1) = 0
故得方程所有解：x=1,x=2,x=3,x=1/2,x=1/3,
全部回答
- 1楼网友：思契十里
- 2021-01-13 10:42
6x^5-41x^4+97x^3-97x^2+41x-6=（3X-1）（2X-1）（X-1）（X-2）（X-3）=0
所以X=1/3 ， 1/2， 1， 2 或3
所以X=1/3 ， 1/2， 1， 2 或3
- 2楼网友：醉吻情书
- 2021-01-13 09:06
6x^5-41x^4+97x^3-97x^2+41x-6
=(6x^5-6)-(41x^4-41x)+(97x^3-97x^2)
=6(x-1)(x^4+x^3+x^2+x+1)-41x(x-1)(x^2+x+1)+97x^2(x-1)
=(x-1)(6x^4-35x^3+62x^2-35x+6)
=(x-1)(3x^2-7x+2)(2x^2-7x+3)
=(x-1)(3x-1)(x-2)(2x-1)(x-3)
所以方程的解为1;1/3;2;1/2;3
=(6x^5-6)-(41x^4-41x)+(97x^3-97x^2)
=6(x-1)(x^4+x^3+x^2+x+1)-41x(x-1)(x^2+x+1)+97x^2(x-1)
=(x-1)(6x^4-35x^3+62x^2-35x+6)
=(x-1)(3x^2-7x+2)(2x^2-7x+3)
=(x-1)(3x-1)(x-2)(2x-1)(x-3)
所以方程的解为1;1/3;2;1/2;3
- 3楼网友：走死在岁月里
- 2021-01-13 08:23
6x^5 - 41x^4 + 97x^3 - 97x^2 + 41x - 6 = 0
6x^5 - 6 - 41x^4 + 41x + 97x^3 - 97x^2 = 0
6(x^5 - 1) - 41x(x³ - 1) + 97x²(x - 1) = 0
(x - 1)*(6x^4 - 35x³ + 6*x² - 35x + 6) = 0
…………
(x - 1)*(x - 2)*(x - 3)*(3x - 1)*(2x - 1) = 0
x = 1 x = 2 x = 3 x = 1/2 x = 1/3
6x^5 - 6 - 41x^4 + 41x + 97x^3 - 97x^2 = 0
6(x^5 - 1) - 41x(x³ - 1) + 97x²(x - 1) = 0
(x - 1)*(6x^4 - 35x³ + 6*x² - 35x + 6) = 0
…………
(x - 1)*(x - 2)*(x - 3)*(3x - 1)*(2x - 1) = 0
x = 1 x = 2 x = 3 x = 1/2 x = 1/3
我要举报
如以上问答信息为低俗、色情、不良、暴力、侵权、涉及违法等信息，可以点下面链接进行举报！
大家都在看
推荐资讯