紧急求助：解数学题4

来源：百度知道 编辑：UC知道 时间：2024/06/16 11:46:07
Given that the coeffisient of x and x² in the expansion of (1+ax+bx² )(1-x)^6 are -4 and 0 respectively, find the value of a and b.

题目:(1+ax+bx^2)*(1-x)^6的展开式中,x和x^2的系数分别为-4和0,求a和b的值.
答案:a=-2,b=-3
解:(利用二项式定理展开)
(1-x)^6=1-6x+15x^2-…+1
(1+ax+bx^2)*(1-x)^6的展开式中x的系数=1×(-6)+a×1=-4①
(1+ax+bx^2)*(1-x)^6的展开式中x^2的系数=1×15+a×(-6)+b×1=0②
由①②式得a=-2,b=-3.

我英语不好