Find the values of a, if the coefficient of x^2 in the expansion (1+ax)^4(2-x)^3 is 6​

Question

Find the values of a, if the
coefficient of x^2 in the
expansion (1+ax)^4(2-x)^3 is 6​

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Thu Hương 1 year 2021-08-22T00:41:14+00:00 1 Answers 5 views 0

Answers ( )

    0
    2021-08-22T00:43:04+00:00

    Step-by-step explanation:

    (1 + ax)⁴(2 – x)³ = (1 + 2ax + a²x²)²(8 – 12x + 6x² – x³) =

    (1 + 4a²x² + a⁴x⁴ + 4ax + 2a²x² + 4a³x³)(8 – 12x + 6x² – x³) = … 6x² + 32a²x² – 48ax² + 16ax² …

    = … x²(6 + 32a² – 32a) …

    32a² – 32a + 6 = 6

    32a(a – 1) = 0 → 32a = 0 → a = 0 OR a – 1 = 0 → a = 1

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