Question

已知a，b，c是一个三角形的三条边长，化简：a-b-c的绝对值+b-a-c的绝对值-c-a+b的绝对值

Answer 1

已知a，b，c是一个三角形的三条边长，即a>0，b.0，c>0,b+c>a,a+b>c,a+c>b,
所以∣a-b-c∣=b+c-a;∣b-a-c∣=a+c-b;∣c-a+b∣=c-a+b,
∣a-b-c∣+∣b-a-c∣-∣c-a+b∣=b+c-a+a+c-b-c+a-b=c+a-b

Answer 2

，∣a-b-c∣=b+c-a;∣b-a-c∣=a+c-b;∣c-a+b∣=c+b-a
∣a-b-c∣+∣b-a-c∣-∣c-a+b∣=b+c-a+a+c-b-c-b+a=c+a-b

Answer 3

答，∣a-b-c∣=b+c-a;∣b-a-c∣=a+c-b;∣c-a+b∣=c+b-a
∣a-b-c∣+∣b-a-c∣-∣c-a+b∣=b+c-a+a+c-b-c-b+a=c+a-b

Answer 4

答：依题意，∣a-b-c∣=b+c-a;∣b-a-c∣=a+c-b;∣c-a+b∣=c+b-a
∣a-b-c∣+∣b-a-c∣-∣c-a+b∣=b+c-a+a+c-b-c-b+a=c+a-b