Question

急求！！高一数学题

x+y=12 xy=9 x小于y 求 x^二分之一+y^二分之一分之x^二分之一-y^二分之一

Answer 1

x>0,y>0否则式子无意义
x-y=((x+y)^2-4xy)^1/2
=6√3
(x^1/2)-(y^1/2) /(x^1/2)+(y^1/2)
=((x^1/2)-(y^1/2))((x^1/2)+(y^1/2)) / (x^1/2)+(y^1/2) ((x^1/2)+(y^1/2) )
=(x-y)/(x+y+2(xy)^1/2)
=6√3/(12+2*3)
=√3/3

Answer 2

原式=(√x-√y)/(√x+√y)
取平方=|（x+y-2√(xy)）/(x+y+2√(xy))|
=1/3
x<y
所以原式<0
则原式= -1/√3

Answer 3

buhiui

Answer 4

x>0,y>0
否则式子无意义
x-y=((x+y)^2-4xy)^1/2
=6√3
(x^1/2)-(y^1/2) /(x^1/2)+(y^1/2)
=6√3/(12+2*3)
=√3/3