设△ABC所对的边为abc,若C=2(A+B)则下列正确的是 c^2小于3ab c^2小于等于3ab c^2大于3ab c^2大于等于3ab

问题描述:

设△ABC所对的边为abc,若C=2(A+B)则下列正确的是 c^2小于3ab c^2小于等于3ab c^2大于3ab c^2大于等于3ab

C+(A+B)=180°
C+C/2=180°
C=120°
cosC=-1/2
c²=a²+b²-2abcosC=a²+b²+ab=(a-b)²+3ab
故c²≥3ab