题目

（1）因式分解 x²-2xy+y²-5x+5y-6 (2)用简便运算 (1-1/2²)(1-1/3²)(1-1/4²)……(1-1/2002²)(1-1/2003²)

提问时间：2020-10-30

答案

（1）因式分解 x²-2xy+y²-5x+5y-6
=(x-y)²-5(x-y)-6
=(x-y-6)(x-y+1)
(2)用简便运算 (1-1/2²)(1-1/3²)(1-1/4²)……(1-1/2002²)(1-1/2003²)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)……(1-1/2002)(1+1/2002)(1-1/2003)(1+1/2003)
=1/2 × 3/2×2/3 × 4/3×3/4 × …… × 2002/2003 × 2004/2003
=1/2 ×2004/2003
=1002/2003