Question

比較x⁶+1與x⁴+x²的大小,其中x∈R.

Answer 1

解析:(x⁶+1)-(x⁴+x²)=x⁶-x⁴-x²+1=x⁴(x²-1)-(x²-1)

=(x²-1)(x⁴-1)=(x²-1)(x²-1)(x²+1)=(x²-1)²(x²+1),

當x=±1時,x⁶+1=x⁴+x²,

當x≠±1時,x⁶+1＞x⁴+x².