tìm x biết lx+1/2l+lx+1/6l+lx+1/12l+….+lx+1/110l=11x

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tìm x biết lx+1/2l+lx+1/6l+lx+1/12l+….+lx+1/110l=11x

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Piper 1 năm 2021-12-07T14:07:46+00:00 2 Answers 1 views 0

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    0
    2021-12-07T14:08:47+00:00

    `|x+1/2|+|x+1/6|+…+|x+1/110|=11x`

    VÌ `|x+1/2|≥0 ; |x+1/6|≥0 ;…;|x+1/110|≥0`

    Nên `|x+1/2|+|x+1/6|+…+|x+1/110|≥0`

    Suy ra `11x≥0`

        `⇒x≥0`

    Ta có:  `x+1/2+x+1/6+…+x+1/110=11x`

        `⇒10x+(1/(1×2)+1/(2×3)+…+1/(10×11)=11x`

        `⇒10x+(1-1/2+1/2-1/3+…+1/10-1/11)=11x`

        `⇒10x+(1-1/11)=11x`

        `⇒x=10/11`

     

    0
    2021-12-07T14:09:33+00:00

    Đáp án:

    `|x+1/2|+|x+1/6|+|x+1/12|+….+|x+1/110|=11x`       `(1)`

    Vì `VT>=0 ∀x`

    `=> VP>=0 ∀x`

    `=> 11x>=0 ∀x`

    `=> x >=0 ∀x`

    `=> x+1/2>0 ∀x, x+1/6 >0 ∀x, x+1/12 >0 ∀x, …. , x+1/(110) >0 ∀x`

    `(1)` `=> x+1/2+x+1/6+….+x+1/110=11x`

    `=> (x+x+…+x)+(1/2+1/6+…+1/110)=11x`

    `=> (x+x+…+x)+(1/(1.2)+1/(2.3)+…+1/(10.11))=11x`

    `=> 10x+(1/1-1/11)=11x`

    `=> 10x+10/11=11x`

    `=> 10/11=11x-10x`

    `=> 10/11=x`

    Vậy `x=10/11`

    < Bài này cô đã chữa, bạn yên tâm tham khảo ^-^ >

     

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