Question

(2008-a)(2007-a)=2003 求 (2008-a)^2-(2007-a)^2的值

Answer 1

设2008-a=x 2007-a=y则 xy=2003 x-y=1

(x-y)^2 =x^2 + y^2 - 2 xy 所以x^2 + y^2可求得1+2003*2=4007

(x^2+y^2)^2=x^4 + y^4 + 2 x^2y^2

(x^2-y^2)^2=x^4 + y^4 - 2 x^2y^2 = x^4 + y^4 + 2 x^2y^2 - 4 x^2y^2

=(x^2+y^2)^2 - 4 x^2y^2=4007^2-4*2003^2

x^2-y^2=2834.1