a²+2b²=3
a²/3+2b²/3=1
(a/√3)²+[√(2/3)b]²=1
由题意,令a/√3=cosx,√(2/3)b=sinx
a=√3cosx b=√(3/2)sinx
a+2b=√3cosx+√6sinx=√(3+6)sin(x+ π/4)=3sin(x+ m),其中tanm=√2
当sin(x+ π/4)=1时,a+2b有最大值3.厉害