(Math Quiz 10 – CT) In the expansion ({left( {x + frac{2}{{sqrt x }}} right)^6}), the coefficient of ({x^3},left( {x) > 0} right)) is:

  • Question:

    In the expansion \({\left( {x + \frac{2}{{\sqrt x }}} \right)^6}\), the coefficient of \({x^3},\left( {x) > 0} \right)\) is:

    Reference explanation:

    Correct answer:

    The general term in the above expansion is

    \({T_{k + 1}} = C_6^k. {x^{6 – k}}{2^k}. {x^{ – \frac{1}{2}k}}\)

    Requires the problem to occur when

    \(6 – k – \frac{1}{2}k = 3 \Leftrightarrow k = 3\)

    Then the coefficient of x3 is: \(C_6^3{.2^3} = 160\).


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