`((-x^2 + 2xy – y^2)/(x + y)) = ((……)/(y^2 – x^2))`

2 bình luận về “`((-x^2 + 2xy – y^2)/(x + y)) = ((……)/(y^2 – x^2))`”

1. (-x^2 + 2xy – y^2)/(x + y) = A/(y^2 – x^2)

   => A = ( (-x^2 +2xy – y^2)(y^2 – x^2))/(x + y)

             = -( (y – x)^2 . (y – x) . (x + y))/(x + y)

             = – (y – x)^3

               = -(y^3 – 3xy^2 + 3x^2y – x^3)

               =x^3 –  3x^2y + 3xy^2 – y^3

    

   Trả lời
2. Gọi số cần tìm là A
   Ta có : ( (-x^2+2xy-y^2)/(x+y) ) = ( A/(y^2-x^2) ) 
   -> A . ( x + y ) = ( -x^2 + 2xy – y^2 ) . ( y^2 – x^2 ) 
   -> A . ( x + y ) = – ( x^2 – 2xy + y^2 ) . ( y – x ) . ( y + x ) 
   -> A . ( x + y ) = -( x – y )^2 . ( y – x ) . ( y + x ) 
   -> (A.(x+y))/(x+y) = (-( x – y )^2 . ( y – x ))/(y+x) 
   -> A = – ( y – x )^3
   -> A = – ( y^3 – 3 . y^2 . x + 3 . y . x^2 – x^3 ) 
   -> A = -y^3 + 3xy^2 – 3x^2y + x^3
    

   Trả lời