Cho `(3x – 2y)/4 = (2z – 4x)/3 = (4y – 3z)/2` chứng minh `x/2 = y/3 = z/4`

Question

Cho `(3x – 2y)/4 = (2z – 4x)/3 = (4y – 3z)/2`
chứng minh `x/2 = y/3 = z/4`

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Mộc Miên 9 months 2021-04-15T13:21:52+00:00 1 Answers 27 views 0

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    2021-04-15T13:23:09+00:00

    (3x – 2y)/4 = (2z – 4x)/3 = (4y – 3z)/2`

    `=> (12x – 8y)/4 = (6z – 12x)/3 = (8y – 6z)/2 = (12x – 8y)/4 + (6z – 12x)/3 + (8y – 6z)/2 = (12x – 8y+6z – 12x+8y – 6z)/(4+3+2) = 0/(4+3+2) = 0`

    `=> 3x – 2y = 2z – 4x = 0`

    `=> 3x = 2y;2z = 4x`

    `=> x/2 = y/3; z/4 = x/2`

    `=> x/2 = y/3 = z/4 (ĐPCM)`

    (Chúc bạn học tốt)

     

     

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