Y=2x^2+3mx+2m
=2[x^2+3mx/2+(3m/4)^2]-9m^2/8+2m
=2(x+3m/4)^2-9m^2/8+2m
所以Y=2x^2+3mx+2m的最小值是-9m^2/8+2m
因为已知Y=2x^2+3mx+2m的最小值是8/9
所以-9m^2/8+2m=8/9
即81m^2-144m+64=0
解得m=8/9
Y=2x^2+3mx+2m
=2[x^2+3mx/2+(3m/4)^2]-9m^2/8+2m
=2(x+3m/4)^2-9m^2/8+2m
所以Y=2x^2+3mx+2m的最小值是-9m^2/8+2m
因为已知Y=2x^2+3mx+2m的最小值是8/9
所以-9m^2/8+2m=8/9
即81m^2-144m+64=0
解得m=8/9