已知(x^2+1)(x-1)^9=a0+a1x+a2x^2+……a11x^11 求(a1+3a3+……+11a11)^2-(2a2+4a4+……+10a10)^2
问题描述:
已知(x^2+1)(x-1)^9=a0+a1x+a2x^2+……a11x^11 求(a1+3a3+……+11a11)^2-(2a2+4a4+……+10a10)^2
答
[(x^2+1)(x-1)^9]的导函数为a1+2*a2*x+3*a3*x^2+.+11*a11*x^10=2x(x-1)^9+9(x-1)^8(x^2+1)令x=1,得a1+2a2+3a3+.+11a11=0令x=-1,得-a1+2a2-3a3+.-11a11=-256两式相加,得2a2+4a4+……+10a10=-128则a1+3a3+……+11a...