有冇人知點解四個連續自然數
乘埋之後，個ａｎｓ再加１
一定係個完全平方數
知ｇｅ唔該詳細解釋
為什麼四個連續自然數的積再加１，一定是個完全平方數？
2006-12-15 4:59 am
回答 (2)
2006-12-15 5:07 am
✔ 最佳答案
Let the smallest one be xx(x+1)(x+2)(x+3) + 1
= (x^2+x)(x^2+5x+6)+1
= x^4+6x^3+11x^2+6x+1
= (x^2+3x+1)^2
which is a complete square
2006-12-15 5:12 am
n(n+1)(n+2)(n+3) +1
=n(n^2 +3n +2)(n+3) +1
=n(n^3 +6n^2 +11n +6) +1
=n^4 +6n^3 +11n^2 +6n +1
=(n^2 +3n +1)^2
=n(n^2 +3n +2)(n+3) +1
=n(n^3 +6n^2 +11n +6) +1
=n^4 +6n^3 +11n^2 +6n +1
=(n^2 +3n +1)^2
收錄日期: 2021-04-28 13:20:30
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20061214000051KK03960