1/a+1/b<=4,(a+b)≤4ab
(a-b)^2=16(ab)^3, a²+b²=2ab+16(ab)^3
(a+b)²=4ab+16(ab)^3≥a+b+16*(a+b)^3/4^3
a+b>0
a+b≥1+(a+b)²/4
(a+b)²-4(a+b)+4≤0
(a+b-2)²≤0
所以a+b-2=0,即：a+b=2