Question

[Pham Trong Bach]

Cho x + y + z ≠ 0 và x = y + z. Chọn đáp án đúng

A.  $\frac{{(xy+yz+zx)}^2-(x^2{y}^2+y^2{z}^2+z^2{x}^2)}{x^2+y^2+x^2}:\frac{{(x+y+z)}^2}{x^2+y^2+z^2}=xy$

B.  $\frac{{(xy+yz+zx)}^2-(x^2{y}^2+y^2{z}^2+z^2{x}^2)}{x^2+y^2+x^2}:\frac{{(x+y+z)}^2}{x^2+y^2+z^2}=yz$

C.  $\frac{{(xy+yz+zx)}^2-(x^2{y}^2+y^2{z}^2+z^2{x}^2)}{x^2+y^2+x^2}:\frac{{(x+y+z)}^2}{x^2+y^2+z^2}=xyz$

D.  $\frac{{(xy+yz+zx)}^2-(x^2{y}^2+y^2{z}^2+z^2{x}^2)}{x^2+y^2+x^2}:\frac{{(x+y+z)}^2}{x^2+y^2+z^2}=1$

Answer 1

[Cao Minh Tâm]

( x y + y z + z x ) 2 − ( x 2 y 2 + y 2 z 2 + z 2 x 2 ) x 2 + y 2 + x 2 : ( x + y + z ) 2 x 2 + y 2 + z 2 =   x 2 y 2 + y 2 z 2 + z 2 x 2 + 2 ( x y 2 z + z 2 y z + y 2 z x ) − ( x 2 y 2 + y 2 z 2 + z 2 x 2 ) x 2 + y 2 + z 2 . x 2 + y 2 + z 2 ( x + y + z ) 2 =   2 x y z ( x + y + z ) ( x + y + z ) 2 = 2 x y z ( x + y + z ) = 2 x y z 2 x = y z

Đáp án cần chọn là: B