a2+b2+c2=4−abc≤4a2+b2+c2=4−abc≤4
Smax=4Smax=4 khi 1 trong 3 số bằng 0
4=abc+a2+b2+c2≥abc+33√(abc)24=abc+a2+b2+c2≥abc+3(abc)23
Đặt 3√abc=x>0⇒x3+3x2−4≤0abc3=x>0⇒x3+3x2−4≤0
⇔(x−1)(x+2)2≤0⇒x≤1⇔(x−1)(x+2)2≤0⇒x≤1
⇒abc≤1⇒S=4−abc≥3⇒abc≤1⇒S=4−abc≥3
Dấu "=" xảy ra khi a=b=c=1