4(a³+b³)=(a+b)[(a+b)²-3ab]
=(a+b){(a+b)²-3[(a+b)²-(a-b)²]/4}
=(a+b)[(a+b)²/4+3(a-b)²/4]≥(a+b)³/4
(a+b)²=a³+b³≥(a+b)³/4
=>a+b≤4
则a只能等于1,2,3
代入可得(a=1,b=2)(a=2,b=1)(a=2,b=2)