Tính x x + 56/2012 + x + 56/2013 = x + 56/2014 + x + 56/2015

Question

Tính x
x + 56/2012 + x + 56/2013 = x + 56/2014 + x + 56/2015

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Caroline 2 tháng 2021-10-19T15:43:51+00:00 2 Answers 2 views 0

Answers ( )

    0
    2021-10-19T15:45:13+00:00

    #
    `(x + 56)/2012 + (x + 56)/2013 = (x + 56)/2014 + (x + 56)/2015 (x ∈ Z)`

    `-> (x + 56)/2012 + (x + 56)/2013 – (x + 56)/2014 – (x + 56)/2015 = 0` (cd- đv)

    `-> (x + 56) . (1/2012 + 1/2013 – 1/2014 – 1/2015) = 0`

    `-> x + 56 = 0` (vì `1/2012 + 1/2013 – 1/2014 – 1/2015 \ne 0`)

    `-> x = 0 – 56`

    `-> x = -56` (TM)

    Vậy `x = -56`

    0
    2021-10-19T15:45:23+00:00

    Đáp án + Giải thích các bước giải:

    Ta có :

    `(x+56)/(2012)+(x+56)/(2013)=(x+56)/(2014)+(x+56)/(2015)`

    `⇔(x+56)/(2012)+(x+56)/(2013)-(x+56)/(2014)-(x+56)/(2015)=0`

    `⇔(x+56)((1)/(2012)+(1)/(2013)-(1)/(2014)-(1)/(2015))=0`

    `⇔x+56=0` . Do `((1)/(2012)+(1)/(2013)-(1)/(2014)-(1)/(2015))\ne0`

    `⇔x=-56`

    Vậy `S={-56}`

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