(x2-x-2)6=a12x12+a11x11+a10x10+…+a1x +a0,则a12+a10+a8+a6+a4+a2=_.

问题描述:

(x2-x-2)6=a12x12+a11x11+a10x10+…+a1x +a0,则a12+a10+a8+a6+a4+a2=______.

把x=0代入得a0=(-2)6=64,把x=1代入得a12+a11+a10+…+a2+a1+a0=(1-1-2)2=64,把x=-1代入得a12-a11+a10+…+a2-a1+a0=(1+1-2)2=0,所以2a12+2a10+2a8+2a6+2a4+2a2+2a0=64,所以a12+a10+a8+a6+a4+a2=12(64-2×64...