解一元一次方程 (x-2)/3+(x-3)/5+(x-2)/7+(x-5)/9+(x-1)/11=18 ，求 x

xfhaoym

这是一道有趣的题：求x的值

Treenewbee

目测x=23时，恰好分子分母可以约分并且两边相等

Future_maths

\(\left( \frac{x-2}{3}-7\right)+\left( \frac{x-3}{5}-4\right)+\left( \frac{x-2}{7}-3\right)+\left( \frac{x-5}{9}-2\right)+\left( \frac{x-1}{11}-2\right)=0\)

Future_maths

\(\left( x-23\right)\left( \frac{1}{3}+\frac{1}{5}+\frac{1}{7}+\frac{1}{9}+\frac{1}{11}\right)=0\)

Future_maths

\(\therefore\ x=23\)

Future_maths

网上有很多这样的题型

haifeng2017

以下使用 Calculator 计算.

如果知道 x 是整数, 则使用下面的 solve() 函数求解. solve() 的用法可以通过 help(solve) 查看.

>> solve((x-2)/3+(x-3)/5+(x-2)/7+(x-5)/9+(x-1)/11==18,x,1,100)
in> solve((x-2)/3+(x-3)/5+(x-2)/7+(x-5)/9+(x-1)/11~18,x,1,100)
ans>> x=23

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方法二

先切换至分数计算模式
>> :mode=fraction

然后直接计算

>> (x-2)/3+(x-3)/5+(x-2)/7+(x-5)/9+(x-1)/11
in> (x-2)/3+(x-3)/5+(x-2)/7+(x-5)/9+(x-1)/11

out> (11*9*7*5*x+11*9*7*3*x+11*9*15*x+11*105*x-21912+945*x-945)|10395

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>> (x-2)/3+(x-3)/5+(x-2)/7+(x-5)/9+(x-1)/11-18
in> (x-2)/3+(x-3)/5+(x-2)/7+(x-5)/9+(x-1)/11-18

out> (11*9*7*5*x+11*9*7*3*x+11*9*15*x+11*105*x+945*x-22857-187110)|10395

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>> 11*9*7*5*x+11*9*7*3*x+11*9*15*x+11*105*x+945*x-22857-187110
in> 11*9*7*5*x+11*9*7*3*x+11*9*15*x+11*105*x+945*x-22857-187110

out> (3465*x+2079*x+1485*x+1155*x+945*x-22857-187110)

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>> simplify(3465x+2079x+1485x+1155x+945x-22857-187110)
in> simplify(3465x+2079x+1485x+1155x+945x-22857-187110)
out> 9129x^1-209967

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>> 209967/9129
in> 209967/9129

out> 23

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By Calculator

波斯猫猫

解方程:
（x＋1）／3＋（x＋2）／5＋（x＋5）／7＋（x＋4）／9＋（x＋10）／11＝x。

haifeng2017

>> :mode=fraction
Switch into fraction calculating mode.
e.g., 1/2+1/3 will return 5/6

>> (x+1)/3+(x+2)/5+(x+5)/7+(x+4)/9+(x+10)/11-x
in> (x+1)/3+(x+2)/5+(x+5)/7+(x+4)/9+(x+10)/11-x

out> (11*9*7*5*x+11*9*7*3*x+11*9*15*x+11*105*x+945*x+29118-10395*x)|10395

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>> 11*9*7*5*x+11*9*7*3*x+11*9*15*x+11*105*x+945*x+29118-10395*x
in> 11*9*7*5*x+11*9*7*3*x+11*9*15*x+11*105*x+945*x+29118-10395*x

out> (3465*x+2079*x+1485*x+1155*x+945*x+29118-10395*x)

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>> simplify(3465*x+2079*x+1485*x+1155*x+945*x+29118-10395*x)
in> simplify(3465*x+2079*x+1485*x+1155*x+945*x+29118-10395*x)
out> -1266x^1+29118

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>> 29118/1266
in> 29118/1266

out> 23

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=====================================
用 solve() 验证

>> solve((x+1)/3+(x+2)/5+(x+5)/7+(x+4)/9+(x+10)/11==x,x,1,100)
in> solve((x+1)/3+(x+2)/5+(x+5)/7+(x+4)/9+(x+10)/11~x,x,1,100)
ans>> x=23

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