灵鹊做题网怎么解（60-x)^0.75=0.4(x-40)
来源：学生作业帮 编辑：灵鹊做题网作业帮 分类：综合作业 时间：2024/04/28 03:12:17
怎么解（60-x)^0.75=0.4(x-40)
（60-x)^0.75=0.4(x-40)
（60-x)^(3/4)=0.4(x-40)
（60-x)^3=[0.4(x-40)]^4
60^3-3*60^2*x+3*60x^2-x^3=(0.4)^4(x^4-4*40x^3+6*40^2x^2-4*40^3x+40^4)
216000-10800x+180x^2-x^3=0.0256x^4-4.096x^3+245.76x^2-6553.6x+65536
0.0256x^4-4.096x^3+x^3+245.76x^2-180x^2-6553.6x-10800x+65536-216000=0
0.0256x^4-3.096x^3+65.76x^2+4246.4x-150464=0
因为两边曾四次方,所以解出后必须验根.
（60-x)^(3/4)=0.4(x-40)
（60-x)^3=[0.4(x-40)]^4
60^3-3*60^2*x+3*60x^2-x^3=(0.4)^4(x^4-4*40x^3+6*40^2x^2-4*40^3x+40^4)
216000-10800x+180x^2-x^3=0.0256x^4-4.096x^3+245.76x^2-6553.6x+65536
0.0256x^4-4.096x^3+x^3+245.76x^2-180x^2-6553.6x-10800x+65536-216000=0
0.0256x^4-3.096x^3+65.76x^2+4246.4x-150464=0
因为两边曾四次方,所以解出后必须验根.