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: \(C_6^3{.2^3} = 160\).
ADSENSE
=======================
MonToan.com shares with you the practice of multiple-choice tests according to the lesson of MATH 10. Multiple-choice questions with detailed answers help you compare and refer to assess your ability. I wish you all the best and success in your studies.