Answers ( )

  1. hongcuc2
    0
    2021-07-30T07:48:57+00:00
    Reply

    I suppose you just have to simplify this expression.

    (2ˣ⁺² – 2ˣ⁺³) / (2ˣ⁺¹ – 2ˣ⁺²)

    Divide through every term by the lowest power of 2, which would be x + 1 :

    … = (2ˣ⁺²/2ˣ⁺¹ – 2ˣ⁺³/2ˣ⁺¹) / (2ˣ⁺¹/2ˣ⁺¹ – 2ˣ⁺²/2ˣ⁺¹)

    Recall that nª / nᵇ = nª⁻ᵇ, so that we have

    … = (2⁽ˣ⁺²⁾ ⁻ ⁽ˣ⁺¹⁾ – 2⁽ˣ⁺³⁾ ⁻ ⁽ˣ⁺¹⁾) / (2⁽ˣ⁺¹⁾ ⁻ ⁽ˣ⁺¹⁾ – 2⁽ˣ⁺²⁾ ⁻ ⁽ˣ⁺¹⁾)

    … = (2¹ – 2²) / (2⁰ – 2¹)

    … = (2 – 4) / (1 – 2)

    … = (-2) / (-1)

    … = 2

    Another way to get the same result: rewrite every term as a multiple of y = 2ˣ :

    … = (2²×2ˣ – 2³×2ˣ) / (2×2ˣ – 2²×2ˣ)

    … = (4×2ˣ – 8×2ˣ) / (2×2ˣ – 4×2ˣ)

    … = (4y – 8y) / (2y – 4y)

    … = (-4y) / (-2y)

    … = 2

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )