已知三角形ABC的三边长分别为a、b、c且均为整数.

2025-01-01 06:30:52
推荐回答(1个)
回答1:

(1)a+c>b
=>c>b-a=5
=>c>=6
a+b+c=2a+5+c为奇数
c为偶数
则C的最小值为6
(2)(a-b)^2+(a-c)^2+(b-c)^2=6

=>(a-b,a-c,b-c)=(2,1,1)
a>b>c则a-c肯定最大
=>
a-c=2,a-b=b-c=1
=>a=c+2,b=c+1
a+b+c=3c+3<=15
=>c<=4
b+c>a
=>2c+1>c+2
=>c>=2
(c,b,a)=(2,3,4),(3,4,5),(4,5,6)