已知a、b、c为△ABC的三边长,且满足a^2+b^2-8b-10a+41=0,求△ABC中最大边c的取值范围
问题描述:
已知a、b、c为△ABC的三边长,且满足a^2+b^2-8b-10a+41=0,求△ABC中最大边c的取值范围
答
(a-5)^2+(b-4)^2=0
a=5 b=4
5
答
a²+b²-8b-10a+41=a²-10a+25+b²-8b+16=(a-5)²+(b-4)²=0∵(a-5)²≥0,(b-4)²≥0(a-5)²+(b-4)²=0∴ (a-5)²=0,(b-4)²=0∴a=5 b=4又∵a<c...