已知x²+y²=6xy求x-y分之x+y

显示全部楼层 · 2013-4-13 16:07:29

x2+y2=6xyx2+y2+2xy=8xy ,x2+y2-2xy=4xy(x+y)2=8xy,
(x-y)2=4xy∴(x-y)2/(x+y)2=4/8=1/2∵x>y>0∴(x-y)/(x+y)=√2/2如果本题有什么不明白可以追问，如果满意记得采纳如果有其他问题请另发或点击向我求助，答题不易，请谅解，谢谢。祝学习进步！...

千问 · 2013-4-13 16:07:29

x2+y2=6xy先：x2-2xy+y2=4xy
(x-y)2=4xy再 x2+2xy+y2=8xy
(x+y)2=8xy所以：(x-y)/(x+y)=√4xy/√8xy=√2/2...

千问 · 2013-4-13 16:07:29

(x-y)^2=x^2-2xy+y^2=6xy-2xy=4xyx-y=±2根号xy(x+y)^2=x^2+2xy+y^2=6xy+2xy=8xyx+y=2根号2xyx-y分之x+y=±根号2...

千问 · 2013-4-13 16:07:29

将x-y分之x+y平方得：分子上是（x-y)^2=x^2+y^2-2xy=6xy-2xy=4xy分母上是：（x+y)^2=x^2+y^2+2xy=6xy+2xy=8xy所以原式=根号下1/2...