(1)f(x0)=3/2,所以sin(2x+π/6)=1/2.2x0+π/6=2kπ+π/6或2kπ+5π/6,k∈Z.因为x0∈[0,2π),所以x0=0或π或π/3或4π/3.(2)f(x)=2sin2(x+π/12).π/12-m=kπ+π/2,k∈Z最少向右平移7π/12个单位。(3)f(x)=3sin(2x+π/6)=a因为x∈[0,π/2),所以2x+π/6∈[π/6,7π/6)使f(x)=a仅有一个实数解,则3sin(7π/6)解得-3/2