Tìm x: 1, $\frac{1}{3}$ .(x-1)+$\frac{1}{2}$ .(x+2)=0,25 2, x- $\frac{1}{4}$x = 60 – x + $\frac{1}{4}$x 3, $\frac{1}{3}$ + $\frac{1}{6}$ + $\frac{1

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1. Đáp án + giải thích bước giải :

   `1) 1/3 (x – 1) + 1/2 (x + 2) = 0,25`

   `-> 1/3x – 1/3 + 1/2x + 1 = 0,25`

   `-> (1/3x + 1/2x) + (-1/3 + 1) = 0,25`

   `-> 5/6x + 2/3 = 0,25`

   `-> 5/6x = (-5)/12`

   `-> x = (-1)/2`

   Vậy `x = (-1)/2`

   `2) x – 1/4x = 60 – x + 1/4x`

   `-> x – 1/4x – 60 + x – 1/4x = 0`

   `-> x (1 – 1/4 + 1 – 1/4) – 60 = 0`

   `-> x . 3/2 = 60`

   `-> x = 60 : 3/2`

   `-> x =40`

   Vậy `x = 40`

   `3) 1/3 + 1/6 + 1/10 + …. + 2/(x (x + 1) ) = 2016/2017`

   `-> 2/6 + 2/12 + 2/20 + … + 2/(x (x + 1) ) = 2016/2017`

   `-> 2 [1/6 + 1/12 + 1/20 +…+ 1/(x (x + 1) )] = 2016/2017`

   `-> 2 [1/(2 . 3) + 1/(3 . 4) + 1/(4 . 5) + … + 1/(x (x + 1) ) ] = 2016/2017`

   `-> 2 [1/2 – 1/3 + 1/3 – 1/4 + 1/4 – 1/5 + … + 1/x – 1/(x + 1) ] = 2016/2017`

   `-> 2 [1/2 + (- 1/3 + 1/3 – 1/4 + 1/4 – 1/5 + … + 1/x) – 1/(x + 1)] = 2016/2017`

   `-> 2 [1/2 – 1/(x + 1)] = 2016/2017`

   `-> 1/2 – 1/(x + 1) = 1008/2017`

   `-> 1/(x + 1) = 1/4034`

   `-> x + 1 = 4034`

   `-> x = 4033`

   Vậy `x = 4033`

   Trả lời

2. Đáp án + Giải thích các bước giải:

   1) `1/3(x – 1) + 1/2(x + 2) = 0,25` $\\$ `=> 1/3x-1/3+1/2x+1=0,25` $\\$ `=> (1/3x+1/2x)+(-1/3+1) = 0,25` $\\$ `=>5/6x +2/3=1/4` $\\$ `=> 5/6x = 1/4 – 2/3 = -5/12` $\\$ `=> x= (-5/12) : 5/6=(-5/12)*6/5=-1/2`

   Vậy `x = -1/2`

   2) `x – 1/4x = 60 – x + 1/4x => x-1/4x-60+x-1/4x=0` $\\$ `=> x+x-1/4x-1/4x-60=0` $\\$ `=> 3/2x-60 = 0 => 3/2x = 60` $\\$ `=> x = 60 : 3/2 = 60*2/3=40`

   Vậy `x = 40`

   3) `1/3 + 1/6 + 1/10 + … + 2/[x(x + 1)] = 2016/2017` $\\$ `=> 2/6+2/12+2/20+…+2/[x(x+1)]=2016/2017` $\\$ `=> 2(1/6 + 1/12 + 1/20 + … + 1/[x(x + 1)])=2016/2017` $\\$ `=> 2(1/(2*3) + 1/(3*4) +1/(4*5)+…+1/[x(x + 1)])=2016/2017` $\\$ `=> 2(1/2-1/3+…+1/x – 1/(x + 1))=2016/2017` $\\$ `=> 2(1/2 – 1/(x + 1)) = 2016/2017` $\\$ `=> 1/2 – 1/(x + 1) = 1008/2017` $\\$ `=> 1/(x + 1) = 1/2 – 1008/2017 = 1/4034` $\\$ `=>x+1 = 4034 => x = 4033`

   Vậy `x = 4033` 

   Trả lời