（x^2+1）(x-2)^9=a0+a1(x-1)+a2(x-1)^2+...+a11(x-1)^11,则(a1+3a3+...+11a11)^2-(2a2+4a4+...+10a10)^2=_________
问题描述：
（x^2+1）(x-2)^9=a0+a1(x-1)+a2(x-1)^2+...+a11(x-1)^11,则(a1+3a3+...+11a11)^2-(2a2+4a4+...+10a10)^2=_________
答
令x=2,左＝0右＝a0+a1+a2+...+a11=0(a1+3a3+...+11a11)^2-(2a2+4a4+...+10a10)^2=(a1+3a3+...+11a11+2a2+4a4+...+10a10)[(a1+3a3+...+11a11)-(2a2+4a4+...+10a10)]=(a1+2a2+3a3+……+9a9+10a10+11a11)(a1-2a2+3a3-4a...