3^2+4^2=5^2,8^2+6^2=10^2,15^2+8^2=17^2,24^2+10^2=26^2.

显示全部楼层 · 2008-7-13 16:48:31

给出一组子:
3^2+4^2=5^2,8^2+6^2=10^2,15^2+8^2=17^2,24^2+10^2=26^2.
(1)第5个式子是什么呢???
(2)用含n的字母表示上述规律~~~
(3)请证明你所发现的规律.

千问 · 2008-7-13 16:48:31

(1) 35^2+12^2=37^2(2)[（n+1）^2-1]^2+[2（n+1）]^2=[（n+1）^2+1]^2(n=1,2,3,4,5……）(3)[（n+1）^2-1]^2+[2（n+1）]^2=[(n+1)^2]^2-2(n+1)^2+1+4(n+1)^2=[(n+1)^2]^2+2(n+1)^2+1=[（n+1）^2+1]^2