Giúp mik vs cb ơi huhuh Cm rằng y/x-y-x^3-xy^2/x^2+y^2.(x/x^2-2xy+y^2-y/x^2-y^2)=1

2 bình luận về “Giúp mik vs cb ơi huhuh Cm rằng y/x-y-x^3-xy^2/x^2+y^2.(x/x^2-2xy+y^2-y/x^2-y^2)=1”

1. Giải đáp + Lời giải và giải thích chi tiết:

   y/(x – y) – (x^3 – xy^2)/(x^2 + y^2) . (x/(x^2 – 2xy + y^2) – y/(x^2 – y^2)) = 1

   VT = y/(x – y) – (x^3 – xy^2)/(x^2 + y^2) . (x/(x^2 – 2xy + y^2) – y/(x^2 – y^2)) (ĐKXĐ : +-x ne +-y)

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

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

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

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

        = y/(x – y) – x/(x – y)

        = -(x – y)/(x – y)

        = -1 ne VT

   Vậy không thể chứng minh.

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2. y/(x-y)-(x^3-xy^2)/(x^2+y^2).(x/(x^2-2xy+y^2)-y/(x^2-y^2)).đkxđ:xne+-y

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

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

   =y/(x-y)-x/(x^2+y^2).(x^2+xy-yx+y^2)/(x-y)

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

   =y/(x-y)-x/(x-y)

   =(y-x)/(x-y)

   =(-(x-y))/(x-y)

   =-1

    

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