作业帮一道分式方程,求方程德正整数解：2/n+3/（n+1)+4/(n+2)=133/60
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一道分式方程,求方程德正整数解：2/n+3/（n+1)+4/(n+2)=133/60
一道分式方程,
求方程德正整数解：
2/n+3/（n+1)+4/(n+2)=133/60
一道分式方程,求方程德正整数解：2/n+3/（n+1)+4/(n+2)=133/60
2/n+3/(n+1)+4/(n+2)=133/60
2(n+1)(n+2)+3n(n+2)+4n(n+1)=133n(n+1)(n+2)/60
60(9n^2+16n+4)=133(n^3+3n^2+2n)
133n^3-141n^2-694n-240=0
133n^3-399n^2+258n^2-774n+80n-240=0
133n^2(n-3)+258n(n-3)+80(n-3)=0
(n-3)(133n^2+258n+80)=0
n-3=0,n=3
133n^2+258n+80=0,△=24004不是完全平方数,无法分解为整数因式.
提示：想象函数
2/n+3/(n+1)+4/(n+2)=133/60
2(n+1)(n+2)+3n(n+2)+4n(n+1)=133n(n+1)(n+2)/60
60(9n^2+16n+4)=133(n^3+3n^2+2n)
133n^3-141n^2-694n-240=0
133n^3-399n^2+258n^2-774n+80n-240=0
133n^2(n-...
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2/n+3/(n+1)+4/(n+2)=133/60
2(n+1)(n+2)+3n(n+2)+4n(n+1)=133n(n+1)(n+2)/60
60(9n^2+16n+4)=133(n^3+3n^2+2n)
133n^3-141n^2-694n-240=0
133n^3-399n^2+258n^2-774n+80n-240=0
133n^2(n-3)+258n(n-3)+80(n-3)=0
(n-3)(133n^2+258n+80)=0
n-3=0，n=3
133n^2+258n+80=0，△=24004不是完全平方数，无法分解为整数因式
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