解方程 (2x+3)(3x-7)(x-6)= -104。請詳細說明答案。
數學知識交流---解方程
2011-08-05 5:45 am
回答 (2)
2011-08-05 6:32 am
✔ 最佳答案
解：(2x+3)(3x-7)(x-6) = -104(6x²-5x-21)(x-6) = -104
6x³ - 41x² + 9x + 230 = 0
6x³ + 12x² - 53x² - 106x + 115x + 230 = 0
6x² (x+2) - 53x (x+2) + 115 (x+2) = 0
(6x² - 53x + 115)(x + 2) = 0
(x - 5)(6x - 23)(x + 2) = 0
所以x1 = 5, x2 = 23/6, x3 = -2.
2011-08-05 6:31 am
(2x+3)(3x-7)(x-6)=104
(6x²-5x-21)(x-6)=104
6x³-41²+9x+126=104
6x³-41²+9x+22=0
x₁=-0.6083546876907349 (16 sig. fig.)
x₂=0.9248657822608948 (16 sig. fig.)
x₃=6.516822338104248 (16 sig. fig.)
(6x²-5x-21)(x-6)=104
6x³-41²+9x+126=104
6x³-41²+9x+22=0
x₁=-0.6083546876907349 (16 sig. fig.)
x₂=0.9248657822608948 (16 sig. fig.)
x₃=6.516822338104248 (16 sig. fig.)
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