phân tich đa thưc thanh nhân tử băng phuong phap đặt an dụ (x+1)(x+3)(x+5)(x+7)+15

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phân tich đa thưc thanh nhân tử băng phuong phap đặt an dụ (x+1)(x+3)(x+5)(x+7)+15

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Khải Quang 2 years 2020-10-18T13:24:11+00:00 2 Answers 93 views 0

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  1. minhkhang
    0
    2020-10-18T13:25:41+00:00
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    $(x+1)(x+3)(x+5)(x+7)+15$

    $=[(x+1)(x+7)][(x+3)(x+5)]+15$
    $=(x^2+8x+7)(x^2+8x+15)+15$
    Đặt `x^2+8x+11=y`

    `=(y-4)(y+4)+15`

    `=y^2-4^2+15`

    `=y^2-1`

    `=(y-1)(y+1)`

    `=(x^2+8x+10)(x^2+8x+12)`

  2. kiet
    0
    2020-10-18T13:26:02+00:00
    Reply

     Giả sử `A=(x+1)(x+3)(x+5)(x+7)+15`

    `=(x^2+8x+7)(x^2+8x+15)+15`

    Đặt `x^2+8x+11=t`

    `=> A=(t-4)(t+4)+15`

    `=t^2-16+15`

    `=t^2-1`

    `=(t-1)(t+1)`

    `=(x^2+8x+10)(x^2+8x+12)`

    `=(x^2+8x+10)(x^2+2x+6x+12)`

    `=(x^2+8x+10)[x(x+2)+6(x+2)]`

    `=(x^2+8x+10)(x+2)(x+6)`

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