(2n-7)^5=(2n-7)^2014

Question

(2n-7)^5=(2n-7)^2014

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Tryphena 8 tháng 2020-10-15T22:25:11+00:00 2 Answers 70 views 0

Answers ( )

  1. `ĐK: n ne 7/2`

    `(2n – 7)^5 = (2n – 7)^{2014}`

    `<=> (2n – 7)^{2014} : (2n – 7)^5 = 1`

    `<=> (2n – 7)^{2009} = 1`

    `<=> 2n – 7 = 1`

    `<=> n = 4`

  2. Vì `5` lẻ và `2014` chẵn nên:

    `(2n-7)^5=(2n-7)^2014`

    $⇒\left[ \begin{array}{l}2n-7=0\\2n-7=1\end{array} \right.$

    $⇒\left[ \begin{array}{l}n=\frac{7}{2}\\n=4\end{array} \right.$

     Vậy `n=4; n=7/2`

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