有四个学生，他们的年龄恰好一个比一个大一岁，他们的年龄的乘积是5040.他们年龄各是多少 有四个学生，他们的年龄恰好是一个比一个大1岁,而他们的年龄的...
\u6709\u56db\u540d\u5b66\u751f\uff0c\u4ed6\u4eec\u7684\u5e74\u9f84\u6070\u597d\u662f\u4e00\u4e2a\u6bd4\u4e00\u4e2a\u5927\u4e00\u5c81\uff0c\u800c\u4ed6\u4eec\u5e74\u9f84\u4e58\u79ef\u662f5040\u90a3\u4e48\u4ed6\u4eec\u7684\u5e74\u9f84\u5404\u662f\u591a\u5c11\uff1f\u4e00:\u8bbe\u6700\u5c0f\u7684\u5b69\u5b50\u5e74\u9f84\u662fx
x*(x+1)*(x+2)*(x+3)=5040
\u4e8c:
\u4f8b10
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\u89e3\uff1a\u6211\u4eec\u5148\u628a5040\u5206\u89e3\u8d28\u56e0\u6570
5040\uff1d24\u00d732\u00d75\u00d77.
\u518d\u628a\u8fd9\u4e9b\u8d28\u56e0\u6570\u51d1\u6210\u56db\u4e2a\u8fde\u7eed\u81ea\u7136\u6570\u7684\u4e58\u79ef\uff1a
24\u00d732\u00d75\u00d77\uff1d7\u00d78\u00d79\u00d710.
\u6240\u4ee5\uff0c\u8fd9\u56db\u540d\u5b66\u751f\u7684\u5e74\u9f84\u5206\u522b\u662f7\u5c81\u30018\u5c81\u30019\u5c81\u548c10\u5c81.
\u3000\u3000\u4e00:\u8bbe\u6700\u5c0f\u7684\u5b69\u5b50\u5e74\u9f84\u662fx
\u3000\u3000x*(x+1)*(x+2)*(x+3)=5040
\u3000\u3000\u4e8c:
\u3000\u3000\u4f8b10 \u6709\u56db\u4e2a\u5b66\u751f\uff0c\u4ed6\u4eec\u7684\u5e74\u9f84\u6070\u597d\u662f\u4e00\u4e2a\u6bd4\u4e00\u4e2a\u59271\u5c81\uff0c\u800c\u4ed6\u4eec\u7684\u5e74\u9f84\u7684\u4e58\u79ef\u662f5040\uff0c\u90a3\u4e48\uff0c\u4ed6\u4eec\u7684\u5e74\u9f84\u5404\u662f\u591a\u5c11\uff1f
\u3000\u3000\u89e3\uff1a\u6211\u4eec\u5148\u628a5040\u5206\u89e3\u8d28\u56e0\u6570
\u3000\u30005040\uff1d24\u00d732\u00d75\u00d77.
\u3000\u3000\u518d\u628a\u8fd9\u4e9b\u8d28\u56e0\u6570\u51d1\u6210\u56db\u4e2a\u8fde\u7eed\u81ea\u7136\u6570\u7684\u4e58\u79ef\uff1a
\u3000\u300024\u00d732\u00d75\u00d77\uff1d7\u00d78\u00d79\u00d710.
\u3000\u3000\u6240\u4ee5\uff0c\u8fd9\u56db\u540d\u5b66\u751f\u7684\u5e74\u9f84\u5206\u522b\u662f7\u5c81\u30018\u5c81\u30019\u5c81\u548c10\u5c81.
\u3000\u3000\u5229\u7528\u5408\u6570\u7684\u8d28\u56e0\u6570\u5206\u89e3\u5f0f\uff0c\u4e0d\u96be\u6c42\u51fa\u8be5\u6570\u7684\u7ea6\u6570\u4e2a\u6570\uff08\u5305\u62ec1\u548c\u5b83\u672c\u8eab\uff09.\u4e3a\u5bfb\u6c42\u4e00\u822c\u65b9\u6cd5\uff0c\u5148\u770b\u4e00\u4e2a\u7b80\u5355\u7684\u4f8b\u5b50.
\u3000\u3000\u6211\u4eec\u77e5\u905324\u7684\u7ea6\u6570\u67098\u4e2a\uff1a1\uff0c2\uff0c3\uff0c4\uff0c6\uff0c8\uff0c12\uff0c24.\u5bf9\u4e8e\u8f83\u5927\u7684\u6570\uff0c\u5982\u679c\u4e00\u4e2a\u4e00\u4e2a\u5730\u53bb\u627e\u5b83\u7684\u7ea6\u6570\uff0c\u5c06\u662f\u5f88\u9ebb\u70e6\u7684\u4e8b.
\u3000\u3000\u56e0\u4e3a24\uff1d23\u00d73\uff0c\u6240\u4ee524\u7684\u7ea6\u6570\u662f23\u7684\u7ea6\u6570\uff081\uff0c2\uff0c22\uff0c23\uff09\u4e0e3\u7684\u7ea6\u6570\uff081\uff0c3\uff09\u4e4b\u95f4\u7684\u4e24\u4e24\u4e58\u79ef.
\u3000\u30001\u00d71\uff0c1\u00d73\uff0c2\u00d71\uff0c2\u00d73\uff0c22\u00d71\uff0c22\u00d73\uff0c23\u00d71\uff0c23\u00d73.
\u3000\u3000\u8fd9\u91cc\u67094\u00d72\uff1d8\u4e2a\uff0c\u5373 \uff083\uff0b1\uff09\u00d7\uff081\uff0b1\uff09\u4e2a\uff0c\u5373\u5bf9\u4e8e24\uff1d23\u00d73\u4e2d\u768423\uff0c\u6709\uff083\uff0b1\uff09\u79cd\u9009\u62e9\uff1a1\uff0c2\uff0c22\uff0c23\uff0c\u5bf9\u4e8e3\u6709\uff081\uff0b1\uff09\u79cd\u9009\u62e9.\u56e0\u6b64\u5171\u6709\uff083\uff0b1\uff09\u00d7\uff081\uff0b1\uff09\u79cd\u9009\u62e9.
\u3000\u3000\u8fd9\u4e2a\u65b9\u6cd5\uff0c\u53ef\u4ee5\u8fd0\u7528\u5230\u4e00\u822c\u60c5\u5f62\uff0c\u4f8b\u5982\uff0c
\u3000\u3000144\uff1d24\u00d732.
\u3000\u3000\u56e0\u6b64144\u7684\u7ea6\u6570\u4e2a\u6570\u662f\uff084\uff0b1\uff09\u00d7\uff082+1\uff09\uff1d15\uff08\u4e2a\uff09.
\u3000\u3000http://www.aoshu.cn/Article_D/2004-04/276134386275382.htm
\u3000\u3000http://www.2itedu.com/shuxue/Article_show.asp?ArticleID=31&ad=0
所以他们年龄各是7 8 9 10岁。
(5040)^(1/4) = 8.4257...
5040 = 8*9*10*7
年龄各是7,8,9,10
5040^0.25约=8，故四人年龄是7、8、9、10
10 9 8 7
绛旓細瑙ｏ細5040=2脳2脳2脳2脳3脳3脳5脳7=7脳8脳9脳10 鎵浠ヤ粬浠骞撮緞鍚勬槸7 8 9 10宀併
绛旓細鏂圭▼涓簒(x+1)(x+2)(x+3)=5040
绛旓細鏁呮纭瓟妗堜负C銆
绛旓細璁剧涓変釜浜虹殑骞撮緞涓篘锛屽彲鍒楁柟绋嬪紡锛氾紙N-2)锛圢-1)N(N+1)=5040=3X3X5X2X2X2X2X7=(3X3)X(5X2)X(2X2X2)X7=9X10X8X7銆 鍥犳锛屼粬浠殑骞撮緞鍒嗗埆鏄7,8,9,10.
绛旓細5040=7脳8脳9脳10锛屼粬浠殑骞撮緞鍒嗗埆鏄7宀侊紝8宀侊紝9宀侊紝10宀併
绛旓細5040=2脳2脳2脳2脳3脳3脳5脳7=7脳8脳9脳10 鎵浠ヤ粬浠骞撮緞鍚勬槸7 8 9 10宀併
绛旓細x*(x+1)*(x+2锛*锛坸+3锛=360. x=3
绛旓細5040=7脳8脳9脳10 鎵浠浠栦滑鏄7宀侊紝8宀侊紝9宀佸拰10宀
绛旓細璁惧洓浜哄勾榫勫垎鍒槸n-1锛沶锛沶+1锛沶+2 n(n+1)*(n-1)(n+2)=3024 (n²+n)*(n²+n-2)=3024 (n²+n)²-2(n²+n)-3024=0 (n²+n-56)(n²+n+54)=0 鍒欙細n²+n-56=0 (n+8)(n-7)=0 n=7 鎵浠锛屼粬浠殑骞撮緞鍒嗗埆鏄細6銆7...
绛旓細涓:璁炬渶灏忕殑瀛╁瓙骞撮緞鏄痻 x*(x+1)*(x+2)*(x+3)=5040 浜:渚10 鏈夊洓涓鐢燂紝浠栦滑鐨勫勾榫勬伆濂鏄涓涓姣斾竴涓ぇ1宀侊紝鑰屼粬浠殑骞撮緞鐨勪箻绉槸5040锛岄偅涔堬紝浠栦滑鐨勫勾榫勫悇鏄灏戯紵瑙ｏ細鎴戜滑鍏堟妸5040鍒嗚В璐ㄥ洜鏁 5040锛24脳32脳5脳7.鍐嶆妸杩欎簺璐ㄥ洜鏁板噾鎴愬洓涓繛缁嚜鐒舵暟鐨勪箻绉細24脳32脳5脳7锛7脳8脳...
