Cho số a dương và [x + căn(x^2+a)][y + căn(y^2+a)] = a. Tính tổng S = x + y

By Trang Ánh Nam -

Cho số a dương và [x + căn(x^2+a)][y + căn(y^2+a)] = a. 
Tính tổng S = x + y

Tính S=x+y.

Giải:

<=>

 

<=>-a.(-a)=

<=>a=

<=>

<=>2x=-2y

<=>x2(y2+a)=y2(x2+a)  (điều kiện x.y≤0)

<=>x2=y2

<=>

ü Với x=y và x.y≤0 =>x=y=0 =>S=0

ü Với x=-y  =>S=x+y=x-x=0

Vậy S=0.

 

 

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