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222-9+11+12:2*14+14 = ? ( )

Toán Lớp 7: cho x , y , z thỏa mãn x / 2013 = y / 2014 = z / 2015 chứng minh rằng ( x – z ) ^ 3 = 8 ( x – y ) ^ 2 . ( y – z )

Tháng Bảy 5, 2022 Toán học 1 Comment 0 views

Toán Lớp 7: cho x , y , z thỏa mãn x / 2013 = y / 2014 = z / 2015 chứng minh rằng ( x – z ) ^ 3 = 8 ( x – y ) ^ 2 . ( y – z )

Comments ( 1 )

  1. kimoanh34
    kimoanh34
    5 Tháng Bảy, 2022 at 12:51 sáng
    Reply
    $\\$
    Đặt x/2013 = y/2014=z/2015=k(k\ne 0)
    =>x=2013k,y=2014k ,z=2015k
    (x-z)^3
    = (2013k – 2015k)^3
    = (-2k)^3
    = -8k^3(1)
    8 (x-y)^2 . (y-z)
    = 8 . (2013k – 2014k)^2 . (2014k – 2015k)
    = 8 . k^2 . (-k)
    = -8 k^3(2)
    (1)(2)
    =>(x-z)^3=8(x-y)^2 (y-z)

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222-9+11+12:2*14+14 = ? ( )

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