(2n²+2n+1)²-(2n²+2n)²
=[(2n²+2n+1)+(2n²+2n)][(2n²+2n+1)-(2n²+2n)]
=(4n²+4n+1)×1
=(2n+1)²
所以(2n²+2n+1)²-(2n²+2n)²=(2n+1)²
所以(2n²+2n+1)²=(2n²+2n)²+(2n+1)²
所以是直角三角形