已知(ax^2+x-b)(ax^2-x+b)-ax(ax^3+x-1)的化简结果中不含x^2项和x项,求b^a
问题描述:
已知(ax^2+x-b)(ax^2-x+b)-ax(ax^3+x-1)的化简结果中不含x^2项和x项,求b^a
答
(ax^2+x-b)(ax^2-x+b)-ax(ax^3+x-1)
=(ax^2+x-b)[ax^2-(x-b)]-ax(ax^3+x-1)
=a^2x^4-(x-b)^2-a^2x^4-ax(x-1)
=(-1-a)x^2+(2b+a)x-b^2
于是a=-1,b=1/2
故b^a=2