已知（x+y）^2=7,(x-y)^2=9,求x^2+y^2=？及xy=?

显示全部楼层 · 2009-1-29 21:14:54

很简单：(x+y)^2=x^2+2xy+y^2(x-y)^2=x^2-2xy+y^2两式相加:(x+y)^2+(x-y)^2=2(x^2+y^2)所以x^2+y^2=16/2=8上两式相减：(x+y)^2-(x-y)^2=4xy所以xy=-2/4=-1/2...

千问 · 2009-1-29 21:14:54

（x+y）^2=7x^2+y^2+2xy=7
(1)(x-y)^2=9x^2+y^2-2xy=9
(2)(1)+(2)x^2+y^2=8(1)-(2)4xy=-2xy=-1/2...

千问 · 2009-1-29 21:14:54

（x+y）^2=7和(x-y)^2=9相减得 4xy=-2,xy=-1/2.（x+y）^2=x^2+y^2+2xy=x^2+y^2-1=7,x^2+y^2=8....

千问 · 2009-1-29 21:14:54

（x+y）^2=x^2+2xy+y^2A(x-y)^2=x^2-2xy+y^2 B两式相加减不就OK啦x^2+y^2=8
xy=-1...