f(x)=x²/2-x+3/2=(x-1)²/2+1
开口向上,对称轴x=1,f(x)在[1,b]上单调递增
则当x有最大值b即x=b时,f(b)=b
b²/2-b+3/2=b,(b＞1)
b²-4b+3=0
(b-1)(b-3)=0
b=3