Question

已知三角形ABC的三边的长分别为m^2-n^2,2mn,m^2+n^2,判断三角形的形状.

Answer 1

a=m^2+n^2

b=m^2-n^2

c=2mn

b^+c^2=(m^2-n^2)^2+(2mn)^2

=m^4-2m^2*n^2+n^4+4m^2*n^2

=m^4+2m^2*n^2+n^4=(m^2+n^2)=a^2

即：b^2+c^2=a^2

所以三角形ABC为直角三角形