2n^2+2n,2n^2+2n-1,2n+1是三角形的三边,能组成直角三角形吗,如果能,那谁是直角边,谁是斜边?

Question

2n^2+2n,2n^2+2n-1,2n+1是三角形的三边,能组成直角三角形吗,如果能,那谁是直角边,谁是斜边?

Answer 1

显然：2n^2+2n>2n^2+2n-1≥2n+1(2n^2+2n)^2-(2n^2+2n-1)^2-(2n+1)^2=-2所以不能为直角三角形若三边为：2n^2+2n,2n^2+2n+1,2n+1,则2n^2+2n+1>2n^2+2n>2n+1(2n^2+2n+1)^2-(2n^2+2n)^2-(2n+1)^2=0所以为直角三角形,且2n...