Question

用换元法判断2000*2002*2004*2006+16是一个完全平方数

Answer 1

设x＝2003

(x-3)(x-1)(x+1)(x+3)+16 = (x^2-1)(x^2-9)+16 = x^4-10x^2 +25

=(x^2-5)^2