已知三角形ABC的边长为a.b.c,且a=m²-n²,b=m²+n²,c=2mn(m>n>0)试判断三角形ABC的形状
问题描述：
已知三角形ABC的边长为a.b.c,且a=m²-n²,b=m²+n²,c=2mn(m>n>0)试判断三角形ABC的形状
答
b^2-a^2
=(m^2+n^2)^2-(m^2-n^2)^2
=(m^4+2m^2n^2+n^4)-(m^4-2m^2n^2+n^4)
=m^4+2m^2n^2+n^4-m^4+2m^2n^2-n^4
=4m^2n^2
=(2mn)^2
=c^2
所以为直角三角形