已知a+b=√(√2005+√2004),a-b=√(√2005-√2004)求ab
问题描述：
已知a+b=√(√2005+√2004),a-b=√(√2005-√2004)求ab
答
a+b=√(√2005+√2004)
(a+b)^2=√2005+√2004
a-b=√(√2005-√2004)
(a-b)^2=√2005-√2004
(a+b)^2-(a-b)^2=a^2+2ab+b^2-a^2-b^2+2ab=4ab
∴ab=(1/4)*[(a+b)^2-(a-b)^2]
=(1/4)*[(√2005+√2004)-(√2005-√2004)]
=(1/2)*√2004