Question

15．已知2009的算术平方根=x算术平方根+y算术平方根,x大于0,y大于x,则满足上式的整数（x,y)有 ---

Answer 1

√2009=√x+√y

2009=x+2√(xy)+y

2√(xy)=2009-x-y

4xy=(2009-x-y)²

4xy=2009²+x²+y²+2xy-4018x-4018y

x²-2xy+y²-4018x-4018y+4036081=0

(x-y)²-4018(x+y)+4036081=0

(x-y)²+4036081=4018(x+y)

二元二次方程有无数组解.整数解有以下几组

x y

0 2009

41 1476

164 1025

369 656