正数x,y满足x^2-y^2=2xy,求(x-y)/(x+y)的值急.
来源:学生作业帮助网 编辑:作业帮 时间:2024/05/15 17:18:54
正数x,y满足x^2-y^2=2xy,求(x-y)/(x+y)的值
急.
(x-y)/(x+y)
=(x-y)(x+y)/[(x+y)^2]
=(x^2-y^2)/[x^2+y^2+2xy]
=2xy/[x^2+y^2+x^2-y^2]
=2xy/(2x^2)
=y/x
x^2-y^2=2xy
x^2-2xy-y^2=0
解出 x=(1+√2)y 或者 x=(1-√2)y
所以原式=y/x=√2-1 或者 -√2-1
解:x^2-y^2=2xy
x^2-2xy+y^2-2y^2=0
(x-y)^2=2y^2
x-y=y*根号2
x=(1+根号2)y
(x,y是正数,所以,x=(1+根号2)y)
将x=(1+根号2)y代入(x-y)/(x+y)中得:
(x-y)/(x+y)=[(1+根号2)y-y]/[(1+根号2)y+y]
=(1+根号2-1)/(...
全部展开
解:x^2-y^2=2xy
x^2-2xy+y^2-2y^2=0
(x-y)^2=2y^2
x-y=y*根号2
x=(1+根号2)y
(x,y是正数,所以,x=(1+根号2)y)
将x=(1+根号2)y代入(x-y)/(x+y)中得:
(x-y)/(x+y)=[(1+根号2)y-y]/[(1+根号2)y+y]
=(1+根号2-1)/(1+根号2+1)
=根号2/2+根号2
=(根号2/2+根号2)*(2-根号2)/(2-根号2)
=根号2*(2-根号2)/2
=(2根号2-2)/2
=根号2-1
收起
视x为主元解一元二次方程;
x^2-2yx-y^2=0
x=(1+根号2)*y(x为正,负根舍去)
(x-y)/(x+y)=(y+根号2*y-y)/(y+根号2*y+y)=根号2-1
正数x,y满足x-y=2xy,求x-y/x+y的值.
正数x,y满足(1+x)(1+y)=2,求xy+1/xy最小值
正数x,y满足x^2-y^2=2xy,求(x-y)/(x+y)的值
正数x,y满足x^2-y^2=2xy,求(x-y)/(x+y)的值急.
正数x、y满足x平方减去y平方=2xy,求(x-y)/(x+y)的值
正数x,y满足x²-y²=2xy,求x-y/x+y的值
正数X,Y满足 X²-Y²=2XY,求X-Y/X+Y的值. 有过程..
正数x,y满足x²-y²=2xy.求x-y/x+y的值
若正数x,y满足x平方-y平方=2xy,求x-y除以x+y的值
正数X Y满足X方-Y方=2XY 求X-Y/X+Y的值
分式正数x,y满足x平方-y平方=2xy,求x-y/x+y等于多少,快
若正数x,y满足xy^2=4 ,求x+2y的最小值.
已知正数xy满足x+2y=2,求1/x+1/y的最小值
正数x、y满足1/x+9/y=1 求xy的最小值?求x+2y的最小值?
正数x、y满足1/x+9/y=1 求xy的最小值?求x+2y的最小值?
正数x、y满足1/x+1/y=1 求xy的最小值?求x+2y的最小值?
正数xy 满足 2/x + 8/y =1 求xy的最小值 求 x + y 的最小值
已知正数x,y满足2x+8y-xy=0,x+y的最小值