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三个质数的倒数的和是231分之131，这三个质数分别是多少

2025-03-15 21:29:14

推荐回答（2个）

回答1：

解：设三个质数为X,Y,Z
依题意，有1/X+1/Y+1/Z=131/231
(X+Y+Z)/XYZ=131/231
可得 X+Y+Z=131
XYZ=231
将231进行分解质因式可得231=3*7*11
故三个质数为3,7,11

回答2：

设三个质数为X,Y,Z
依题意，有1/X+1/Y+1/Z=131/231
(X+Y+Z)/XYZ=131/231
可得 X+Y+Z=131
XYZ=231
将231进行分解质因式可得231=3*7*11
故三个质数为3,7,11

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