试比较[(x的6次方)+1]与[(x的4次方)+(x的二次方)]的大小.
问题描述：
试比较[(x的6次方)+1]与[(x的4次方)+(x的二次方)]的大小.
答
x^6+1-x^4-x^2=x^4(x^2-1)-(x^2-1)=(x^2-1)^2(x^2+1)≥0
答
做差即,
x^6+1-(x^4+x^2)
=x^4(x^2-1)-(x^2-1)
=（x^4-1)(x^2-1)
=(x^2+1)(x^2-1)^2≥0
即x^6+1≥x^4+x^2