Cho a,b,c > 0, CMR : a/ b +c + b/c + a + c/ a + b lớn hơn bằng 3/2
Giải thích
Từ x+y+z1x+1y+1z≥9, Đặt x=a+by=b+cz=c+a
⇒2a+b+c1a+b+1b+c+1c+a≥9⇔a+b+ca+b+a+b+cb+c+a+b+cc+a≥92⇒ca+b+ab+c+bc+a≥92−3=32
Từ x+y+z1x+1y+1z≥9, Đặt x=a+by=b+cz=c+a
⇒2a+b+c1a+b+1b+c+1c+a≥9⇔a+b+ca+b+a+b+cb+c+a+b+cc+a≥92⇒ca+b+ab+c+bc+a≥92−3=32