解方程1/(xx+x)+1/(xx+3x+2)+1/(xx+5x+6)+1/(xx+7x+12)+1/(xx+9x+20
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/11 18:28:56
解方程1/(xx+x)+1/(xx+3x+2)+1/(xx+5x+6)+1/(xx+7x+12)+1/(xx+9x+20)=5/(xx+11x-708)
方程左边1/(xx+x)+1/(xx+3x+2)+1/(xx+5x+6)+1/(xx+7x+12)+1/(xx+9x+20)对分母因式分解得
1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+1/(x+4)(x+5)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)+1/(x+4)-1/(x+5)
=1/x-1/(x+5)
=5/x(x+5)
所以原方程可化简得
5/x(x+5)=5/(xx+11x-708)
方程两边同乘以最简公分母得xx+11x-708=x(x+5)
解得x=118
经检验得:x=118是原方程的解
1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+1/(x+4)(x+5)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)+1/(x+4)-1/(x+5)
=1/x-1/(x+5)
=5/x(x+5)
所以原方程可化简得
5/x(x+5)=5/(xx+11x-708)
方程两边同乘以最简公分母得xx+11x-708=x(x+5)
解得x=118
经检验得:x=118是原方程的解
解方程1/(xx+x)+1/(xx+3x+2)+1/(xx+5x+6)+1/(xx+7x+12)+1/(xx+9x+20
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