$\frac{x-90}{10}$ +$\frac{x-76}{12}$+$\frac{x-58}{14}$+$\frac{x-36}{16}$+$\frac{x-15}{17}$=15

Question

$\frac{x-90}{10}$ +$\frac{x-76}{12}$+$\frac{x-58}{14}$+$\frac{x-36}{16}$+$\frac{x-15}{17}$=15

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Eden 3 tuần 2021-08-23T06:31:13+00:00 2 Answers 4 views 0

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    0
    2021-08-23T06:32:31+00:00

    Đáp án:

     

    Giải thích các bước giải:

    $\frac{x-90}{10}$+$\frac{x-76}{12}$+$\frac{x-58}{14}$+$\frac{x-36}{16}$+$\frac{x-15}{17}$ =15 <=>($\frac{x-90}{10}$-1)+$\frac{x-76}{12}$-2)+($\frac{x-58}{14}$-3)+($\frac{x-36}{16}$-4)+($\frac{x-15}{17}$-5) =0 <=>$\frac{x-100}{10}$+$\frac{x-100}{12}$+$\frac{x-100}{14}$+$\frac{x-100}{16}$+$\frac{x-100}{17}$ =0 <=>(x-100).($\frac{1}{10}$+$\frac{1}{12}$+$\frac{1}{14}$+$\frac{1}{16}$+$\frac{1}{17}$ )=0 <=>x-100=0 <=>x=100

    0
    2021-08-23T06:33:05+00:00

    Đáp án:

    `x=100`

    Giải thích các bước giải:

    `(x-90)/10 + (x-76)/12 + (x-58)/14 + (x-36)/16 + (x-15)/17 = 15`

    `<=> (x-90)/10 + (x-76)/12 + (x-58)/14 + (x-36)/16 + (x-15)/17 – 15 = 0`

    `<=> ((x-90)/10 – 1) + ((x-76)/12 – 2) + ((x-58)/14 – 3) + ((x-36)/16 – 4) + ((x-15)/17 – 5)=0`

    `<=> (x-100)/10 + (x-100)/12 + (x-100)/14 + (x-100)/16 + (x-100)/17 = 0`

    `<=> (x-100).(1/10 + 1/12 + 1/14 + 1/16 + 1/17) = 0`

    Do `1/10 + 1/12 + 1/14 + 1/16 + 1/17` $\ne 0$

    `=> x-100 = 0 <=> x=100`

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