首页 > 数学 > 题目详情
【(111+121+131+141)×(121+131+141+151)−(111+121+131+141+151)×(121+131+141)．】
题目内容：
(1 11
+1 21
+1 31
+1 41
)×(1 21
+1 31
+1 41
+1 51
)−(1 11
+1 21
+1 31
+1 41
+1 51
)× (1 21
+1 31
+1 41
)．优质解答
令1 11
+1 21
+1 31
+1 41
=a，1 21
+1 31
+1 41
=b，
则原式=a×（b+1 51
）-（a+1 51
）×b
=ab+1 51
a-ab-1 51
b
=1 51
×（a-b）
=1 51
×[（1 11
+1 21
+1 31
+1 41
）-（1 21
+1 31
+1 41
）]
=1 51
×1 11
=1 561
；
| 1 |
| 11 |
| 1 |
| 21 |
| 1 |
| 31 |
| 1 |
| 41 |
| 1 |
| 21 |
| 1 |
| 31 |
| 1 |
| 41 |
| 1 |
| 51 |
| 1 |
| 11 |
| 1 |
| 21 |
| 1 |
| 31 |
| 1 |
| 41 |
| 1 |
| 51 |
| 1 |
| 21 |
| 1 |
| 31 |
| 1 |
| 41 |
优质解答
| 1 |
| 11 |
| 1 |
| 21 |
| 1 |
| 31 |
| 1 |
| 41 |
| 1 |
| 21 |
| 1 |
| 31 |
| 1 |
| 41 |
则原式=a×（b+
| 1 |
| 51 |
| 1 |
| 51 |
=ab+
| 1 |
| 51 |
| 1 |
| 51 |
=
| 1 |
| 51 |
=
| 1 |
| 51 |
| 1 |
| 11 |
| 1 |
| 21 |
| 1 |
| 31 |
| 1 |
| 41 |
| 1 |
| 21 |
| 1 |
| 31 |
| 1 |
| 41 |
=
| 1 |
| 51 |
| 1 |
| 11 |
=
| 1 |
| 561 |
本题链接：