在三角形ABC中,BC=2n+1,AC=2n^2+2n,AB=2n^2+2n+1,则三角形ABC是直角三角形吗?
试说明理由~
參考答案:BC^2+AC^2
=(2n+1)^2+(2n^2+2n)^2
=4n^4+8n^3+8n^2+4n+1
AB^2
=(2n^2+2n+1)^2
=(2n^2+2n)^2+1+2(2n^2+2n)
=4n^4+8n^3+8n^2+4n+1
BC^2+AC^2
=(2n+1)^2+(2n^2+2n)^2
=4n^4+8n^3+8n^2+4n+1
AB^2=BC^2+AC^2
直角三角形