已知2x+2-x=a(常数),求8x+8-x的值.

问题描述:

已知2x+2-x=a(常数),求8x+8-x的值.

令2x=t,则2-x=t-1,则t+t-1=a.①
法一:由①两边平方得t2+t-2=a2-2,
则8x+8-x=t3+t-3=(t+t-1)(t2-t•t-1+t-2
=a(a2-3)=a3-3a.
法二:8x+8-x=t3+t-3=(t+t-1)[(t+t-12-3t•t-1]
=a(a2-3)=a3-3a.