Toán Lớp 7: Cho dãy tỉ số bằng nhau (mẫu số đều khác 0):`{y+z+t-2020x}/x={z+t+x-2020y}/y={t+x+y-2020z}/z={x+y+z-2020t}/t` Biết `x+y+z+t=2020`. Tính

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Toán Lớp 7:  Cho dãy tỉ số bằng nhau (mẫu số đều khác 0):{y+z+t-2020x}/x={z+t+x-2020y}/y={t+x+y-2020z}/z={x+y+z-2020t}/t Biết x+y+z+t=2020. Tính A=2019x-2020y+2021z-2022t

maingoctruc · Answer

#huy   (y+z+t-2020t)/x=(z+t+x-2020y)/y=(t+x+y-2020z)/z=(x+y+z-2020t)/t(1)   (y+z+t-2020x)/x+2021=(x+y+z+t)/x(2)   (z+t+zx-2020y)/y+2021=(x+y+z+t)/y(3)   (t+x+y-2020z)/z+2021=(x+y+z+t)/z(4)   (x+y+z-2020t)/t+2021=(x+y+z+t)/t(5)   Từ (1);(2);(3);(4);(5) suy ra    (x+y+z+t)/x=(x+y+z+t)/y=(x+y+z+t)/z=(x+y+z+t)/t   <=>x=y=z=t=(x+y+z+t)/4=2020/4=505   A=2029x-2020y+2021z-2022t   =2029x-2020x+2021x-2022x   =-2x=-1010

thucquyenlan · Answer

$  $   &Aacute;p dụng t&iacute;nh chất d&atilde;y tỉ số bằng nhau c&oacute; :   (y+z+t-2020x)/x=(z+t+x-2020y)/y = (t+x+y-2020z)/z=(x+y+z-2020t)/t=(y+z+t-2020x + z+t+x-2020y + t+x+y-2020z + t+x+y-2020z)/(x+y+z+t) = (-2017x -2017y - 2017z - 2017t)/(x+y+z+t) = (-2017 (x+y+z+t))/(x+y+z+t)=-2017   -> y+z+t-2020x=-2017x -> y+z+t=3x -> x+y+z+t=4x   V&agrave; z+t+x-2020y = -2017y -> z+t+x=3y ->x+y+z+t=4y   V&agrave; t+x+y-2020z=-2017z -> t+x+y=3z ->x+y+z+t=4z   V&agrave; x+y+z-2020t=-2017t ->x+y+z=3t ->x+y+z+t=4t   Do đ&oacute; : 4x=4y=4z=4t   ->x=y=z=t   M&agrave; x+y+z+t=2020   ->x=y=z=t=2020/4=505   A=2019x - 2020y+2021z - 2022t   ->A=2019 . 505 - 2020 . 505 + 2021 . 505 - 2022 . 505   -> A=505 . (2019 - 2020 + 2021 - 2022)   ->A=505 . (-2)   ->A=-1010   Vậy A=-1010