Question

设(x+2)^9=a0+a1x+a2x^2+...+a9x^9 求（a1+3a3+5a5+7a7+9a9）^2--（2a

Answer 1

当x＝1时,a0＋a1＋a2＋a3＋a4＋a5＋a6＋a7＋a8＋a9＝19683 ①

当x＝－1时,a0－a1＋a2－a3＋a4－a5＋a6－a7＋a8－a9＝1 ②

当x＝0时,a0＝2^9＝512

①－②得：a1＋a3＋a5＋a7＋a9＝9841

①＋②得：a0＋a2＋a4＋a6＋a8＝9842

a2＋a4＋a6＋a8＝9330

（a1＋a3＋a5＋a7＋a9）²－（a2＋a4＋a6＋a8）²＝9841²－9330²

＝（9841－9330）×（9841＋9330）

＝9796381