191问答库 > 3的平方-1的平方=8=8乘以1,5的平方-3的平方=16=8乘以2,7的平方-5的平方=24=8乘以3把规律用n的式子表示，谢

3的平方-1的平方=8=8乘以1,5的平方-3的平方=16=8乘以2,7的平方-5的平方=24=8乘以3把规律用n的式子表示，谢

2025-03-18 06:21:55
推荐回答（3个）
回答1：

5^2-3^2=8*2

9^2-7^2=8*4

规律就是：二个连续奇数的平方差是8的倍数。

即：(2n+1)^2-(2n-1)^2=8n

证明：(2n+1)^2-(2n-1)^2=(2n+1+2n-1)(2n+1-2n+1)=8n

回答2：

一正一负就是相乘小于0
所以x1x2<0
由韦达定理
x1x2=(2a+6)/1=2a+6<0
a<-3

且判别式大于0
4(a-1)2-4(2a+6)>0
a2-2a+1-2a-6=a2-4a-5>0
(a-5)(a+1)>0
a<-1,a>5
所以a<-3

回答3：

(2n+1)²-(2n-1)²=8n

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