Question

在下列各题的横线上填上适当的不等号.

(1)若x＞0,y＞0,则x³+y³__________x²y+xy².

(2)若x∈R,则(x²+1)³__________x⁶+2x⁴+2x²+1.

Answer 1

解析：(1)x³+y³-x²y-xy²=x²(x-y)+y²(y-x)=(x-y)(x²-y²)=(x-y)²(x+y)≥0.

(2)(x²+1)³-(x⁶+2x⁴+2x²+1)=x⁶+3x⁴+3x²+1-x⁶-2x⁴-2x²-1=x⁴+x²≥0.

答案：(1)≥  (2)≥