x + 1 / x^2 + x + 1 – x – 1 / x^2 – x + 1 = 3 / x . ( x ^4 + x^2 + 1 )

Question

x + 1 / x^2 + x + 1 – x – 1 / x^2 – x + 1 = 3 / x . ( x ^4 + x^2 + 1 )

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Emery 2 tháng 2021-10-20T02:29:25+00:00 1 Answers 6 views 0

Answers ( )

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    2021-10-20T02:31:16+00:00

    Đáp án:

    `S={3/2}`

    Giải thích các bước giải:

    `x^4+x^2+1`

    `=x^4+2x^2+1-x^2`

    `=(x^2+1)^2-x^2`

    `=(x^2-x+1)(x^2+x+1)`

    `pt<=>(x+1)/(x^2+x+1)-(x-1)/(x^2-x+1)=3/(x(x^2-x+1)(x^2+x+1))(x ne +-1)`

    `<=>x(x+1)(x^2-x+1)-x(x-1)(x^2+x+1)=3`

    `<=>x(x^3+1)-x(x^3-1)=3`

    `<=>2x=3`

    `<=>x=3/2`

    Vậy `S={3/2}`

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