3²-1²=8x1,5²-3²=16=8x2,7²-5²=24=8x3...给出下列算式:3²-1²=8x1,5²-3²=16=8x2,7²-5²=24=8x3,9²-7²=32=8x4,11²-9²=8x5……(1)观察上面一系列数字,你发现
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/27 21:41:14
![3²-1²=8x1,5²-3²=16=8x2,7²-5²=24=8x3...给出下列算式:3²-1²=8x1,5²-3²=16=8x2,7²-5²=24=8x3,9²-7²=32=8x4,11²-9²=8x5……(1)观察上面一系列数字,你发现](/uploads/image/z/1621785-57-5.jpg?t=3%26%23178%3B-1%26%23178%3B%3D8x1%2C5%26%23178%3B-3%26%23178%3B%3D16%3D8x2%2C7%26%23178%3B-5%26%23178%3B%3D24%3D8x3...%E7%BB%99%E5%87%BA%E4%B8%8B%E5%88%97%E7%AE%97%E5%BC%8F%EF%BC%9A3%26%23178%3B-1%26%23178%3B%3D8x1%2C5%26%23178%3B-3%26%23178%3B%3D16%3D8x2%2C7%26%23178%3B-5%26%23178%3B%3D24%3D8x3%2C9%26%23178%3B-7%26%23178%3B%3D32%3D8x4%2C11%26%23178%3B-9%26%23178%3B%3D8x5%E2%80%A6%E2%80%A6%EF%BC%881%EF%BC%89%E8%A7%82%E5%AF%9F%E4%B8%8A%E9%9D%A2%E4%B8%80%E7%B3%BB%E5%88%97%E6%95%B0%E5%AD%97%2C%E4%BD%A0%E5%8F%91%E7%8E%B0)
3²-1²=8x1,5²-3²=16=8x2,7²-5²=24=8x3...给出下列算式:3²-1²=8x1,5²-3²=16=8x2,7²-5²=24=8x3,9²-7²=32=8x4,11²-9²=8x5……(1)观察上面一系列数字,你发现
3²-1²=8x1,5²-3²=16=8x2,7²-5²=24=8x3...
给出下列算式:3²-1²=8x1,5²-3²=16=8x2,7²-5²=24=8x3,9²-7²=32=8x4,11²-9²=8x5……
(1)观察上面一系列数字,你发现了什么规律?
(2)用你观察到得规律,计算2011²-2009²
3²-1²=8x1,5²-3²=16=8x2,7²-5²=24=8x3...给出下列算式:3²-1²=8x1,5²-3²=16=8x2,7²-5²=24=8x3,9²-7²=32=8x4,11²-9²=8x5……(1)观察上面一系列数字,你发现
(1)
规律:(2n+1)²-(2n-1)²=8n
(2)
∴2011²-2009²
=(2*1005+1)²-(2*1005-1)²
=8*1005=8040
X²-(X-2)²=8*(X-2+1)/2 也可以是A²-B²=8*((A+B)/4) 或者是
A²-B²=(A+B)*(A-B)平方差公式
8040
1 (2k+1)²-(2k-1)²=(2k+1+2k-1)(2k+1-2k+1)=(4k)(2)=8k
2 2011²-2009² k=1005
2011²-2009²=8x1005=8040
1)等式左边2个数差2;等式右边与8相乘的数等于右边第一个数减1除2
2)计算式=8X(2011-1)/2=8040
(1)相邻两奇数的平方差等于8与较小奇数加1的和的一半的乘积
(2)2011²-2009²=8*[(2009+1)/2]=8*1005=8040
(1)(2n+1)²-(2n-1)²=8n n为正整数
(2)2011²-2009²
其中2011=2n+1
n=1005
上式=8040
(1)规律如下:
(2*n + 1) ^2 +(2*n - 1)^2 =8*n
(2)
令2011 = 2*n + 1 ,可得 n= 1005,
所以:2011²-2009²= 8*1005