Toán Lớp 8: Cho `x^2+2021y^2=2022xy` và `x+y≠0`. Tính `A=(x-y)/(x+y)`

Question

Toán Lớp 8:  Cho x^2+2021y^2=2022xy và x+y≠0. Tính A=(x-y)/(x+y)

ngoclandiep · Answer

$ $ x^2+2021y^2=2022xy <=>x^2-2022xy + 2021y^2=0 <=> (x^2- xy) - (2021xy + 2021y^2)=0 <=> x (x-y) - 2021 y (x-y) =0 <=>(x-y)(x-2021y)=0 <=> ( left[ begin{array}{l}x-y=0 x-2021y=0 end{array} right. ) <=> ( left[ begin{array}{l}x=y x=2021y end{array} right. ) $ bullet$ x=y =>A=(x-x)/(x+x)=0/(2x)=0 $ bullet$ x=2021y =>A=(2021y-y)/(2021y + y) = (2020y)/(2022y)=1010/1011 Vậy A=0,A=1010/1011

hauthanhyen98 · Answer

Giải đáp:   $x + y  ne 0$   Ta c&oacute; : $x^{2} + 2021y^{2} = 2022xy$   &hArr; $x^{2} - 2022xy + 2021y^{2} = 0$   &hArr; $( x^{2} - xy ) - ( 2021xy - 2021y^{2} ) = 0$   &hArr; $x( x - y ) - 2021y( x - y ) = 0$   &hArr; $( x - y )( x - 2021y ) = 0$   &hArr;  ( left[  begin{array}{l}x=y  x=2021y end{array}  right. )    +) $x = y$   Ta co : $A =  frac{x-y}{x+y}$   &hArr; $A =  frac{y-y}{y+y} $   &hArr; $A =  frac{0y}{2y} = 0$   +) $x = 2021y$   Ta co : $A =  frac{2021y-y}{2021y+y}$   &hArr; $A =  frac{2020y}{2022y} =  frac{1010}{1011}$