观察:3²-1²=8,5²-3²=16,7²-5²=24,9²-7²=32……(1)根据上述规律填空:13²-11²=,19²-17²=;(2)你能用含n的等式表示这个规律吗?并说明它的正确性.
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![观察:3²-1²=8,5²-3²=16,7²-5²=24,9²-7²=32……(1)根据上述规律填空:13²-11²=,19²-17²=;(2)你能用含n的等式表示这个规律吗?并说明它的正确性.](/uploads/image/z/369192-48-2.jpg?t=%E8%A7%82%E5%AF%9F%EF%BC%9A3%26%23178%3B-1%26%23178%3B%3D8%2C5%26%23178%3B-3%26%23178%3B%3D16%2C7%26%23178%3B-5%26%23178%3B%3D24%2C9%26%23178%3B-7%26%23178%3B%3D32%E2%80%A6%E2%80%A6%EF%BC%881%EF%BC%89%E6%A0%B9%E6%8D%AE%E4%B8%8A%E8%BF%B0%E8%A7%84%E5%BE%8B%E5%A1%AB%E7%A9%BA%EF%BC%9A13%26%23178%3B-11%26%23178%3B%3D%2C19%26%23178%3B-17%26%23178%3B%3D%EF%BC%9B%EF%BC%882%EF%BC%89%E4%BD%A0%E8%83%BD%E7%94%A8%E5%90%ABn%E7%9A%84%E7%AD%89%E5%BC%8F%E8%A1%A8%E7%A4%BA%E8%BF%99%E4%B8%AA%E8%A7%84%E5%BE%8B%E5%90%97%3F%E5%B9%B6%E8%AF%B4%E6%98%8E%E5%AE%83%E7%9A%84%E6%AD%A3%E7%A1%AE%E6%80%A7.)
观察:3²-1²=8,5²-3²=16,7²-5²=24,9²-7²=32……(1)根据上述规律填空:13²-11²=,19²-17²=;(2)你能用含n的等式表示这个规律吗?并说明它的正确性.
观察:3²-1²=8,5²-3²=16,7²-5²=24,9²-7²=32……
(1)根据上述规律填空:13²-11²=,19²-17²=;(2)你能用含n的等式表示这个规律吗?并说明它的正确性.
观察:3²-1²=8,5²-3²=16,7²-5²=24,9²-7²=32……(1)根据上述规律填空:13²-11²=,19²-17²=;(2)你能用含n的等式表示这个规律吗?并说明它的正确性.
13²-11²=48
19²-17²=72
规律:(2n+1)²-(2n-1)² =8n
说明:(2n+1)²-(2n-1)²
=(2n+1+2n-1)(2n+1-2n+1)
=4n×2
=8n
(1)根据上述规律填空:13²-11²=48,19²-17²=72;
(2)你能用含n的等式表示这个规律吗?并说明它的正确性。
规律是:﹙2n+1﹚²-﹙2n-1﹚²=8n
﹙2n+1﹚²-﹙2n-1﹚²=4n²+4n+1-4n²+4n-1=8n。...
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(1)根据上述规律填空:13²-11²=48,19²-17²=72;
(2)你能用含n的等式表示这个规律吗?并说明它的正确性。
规律是:﹙2n+1﹚²-﹙2n-1﹚²=8n
﹙2n+1﹚²-﹙2n-1﹚²=4n²+4n+1-4n²+4n-1=8n。
收起
13²-11²=48
19²-17²=72
(2*n+1)^2-(2*n-1)^2=8*n
将式子按照完全平方公式展开得:4n^2+4n+1-4n^2+4n-1=8n
所以式子正确
13²-11²=(13+11)(13-11),19²-17²=(19+17)(19-17),(n+2) ²-n²=2(2n+2)=2²(n+1)