实数xyz满足y+z=6-4x+3x^2,z-y=4-4x+x^2,比较xyz的大小
问题描述:
实数xyz满足y+z=6-4x+3x^2,z-y=4-4x+x^2,比较xyz的大小
答
z-y=4-4x+x^2=(2-x)^2≥0,z≥y
两式y+z=6-4x+3x^2,z-y=4-4x+x^2相减,得y=1+x^2,y-x=x^2-x+1=(x-1/2)^2+3/4>0,y>x
故x