x-1/2014+x-2/2013+x-3/2012=x-10/2005=+x-11/2004+x-12/2003

x-1/2014+x-2/2013+x-3/2012=x-10/2005=+x-11/2004+x-12/2003

0 bình luận về “x-1/2014+x-2/2013+x-3/2012=x-10/2005=+x-11/2004+x-12/2003”

  1. Đáp án :

    `x=2015`

    Giải thích các bước giải :

    `(x-1)/(2014)+(x-2)/(2013)+(x-3)/(2012)=(x-10)/(2005)+(x-11)/(2004)+(x-12)/(2003)`

    `<=>(x-1)/(2014)+(x-2)/(2013)+(x-3)/(2012)-3=(x-10)/(2005)+(x-11)/(2004)+(x-12)/(2003)-3`

    `<=>((x-1)/(2014)-1)+((x-2)/(2013)-1)+((x-3)/(2012)-1)=((x-10)/(2005)-1)+((x-11)/(2004)-1)+((x-12)/(2003)-1)`

    `<=>(x-1-2014)/(2014)+(x-2-2013)/(2013)+(x-3-2012)/(2012)=(x-10-2005)/(2005)+(x-11-2004)/(2004)+(x-12-2003)/(2003)`

    `<=>((x-1-2014)/(2014)+(x-2-2013)/(2013)+(x-3-2012)/(2012))-((x-10-2005)/(2005)+(x-11-2004)/(2004)+(x-12-2003)/(2003))=0`

    `<=>(x-2015)/(2014)+(x-2015)/(2013)+(x-2015)/(2012)-(x-2015)/(2005)-(x-2015)/(2004)-(x-2015)/(2003)=0`

    `<=>(x-2015)(1/(2014)+1/(2013)+1/(2012)-1/(2005)-1/(2004)-1/(2003))=0`

    Vì `1/(2014)+1/(2013)+1/(2012)-1/(2005)-1/(2004)-1/(2003) ≠ 0`

    `=>x-2015=0`

    `<=>x=2015`

    Vậy `x=2015`

    ~Chúc bạn học tốt !!!~

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  2. Đáp án:

    `(x-1)/2014+(x-2)/2013+(x-3)/2012=(x-10)/2005+(x-11)/2004+(x-12)/2003`

    `-> ((x-1)/2014-1)+((x-2)/2013-1)+((x-3)/2012-1)=((x-10)/2005-1)+((x-11)/2004-1)+((x-12)/2003-1)`

    `-> (x-2015)/2014+(x-2015)/2013+(x-2015)/2012=(x-2015)/2005+(x-2015)/2004+(x-2015)/2003`

    `-> (x-2015)/2014+(x-2015)/2013+(x-2015)/2012-(x-2015)/2005-(x-2015)/2004-(x-2015)/2003=0`

    `-> (x-2015).(1/2014+1/2013+1/2012-1/2005-1/2004-1/2003)=0`

    Mà `(1/2014+1/2013+1/2012-1/2005-1/2004-1/2003)\ne0`

    `-> x-2015=0`

    `-> x=2015`

     

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