a^2+4b^2+c^2=1,
因为2ab≤a^2+b^2,2bc≤b^2+c^2,2ca≤c^2+ a^2,
(a+b+c)^2
=a^2+b^2+c^2+2ab+2bc+2ca+3b^2-3b^2
=1+2ab+2bc+2ca-3b^2
<1-3b^2+(a²+b²+b²+c²+c²+a²)
=1+2a²+2c²-b²
=3-9b²
≤3
而(a+b+c)≤√3.(b=0时取到等号)