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Let a and b are two positive real numbers such that $a^{2} + b = 2,$ then the maximum value of the term independent of x in the expansion of ${(a x^{\frac{1}{6}} + b x^{\frac{- 1}{3}})}^{9}$ is

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answer is 84.

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Detailed Solution

Term independent of $x = {}^{9}C_{3} a^{6} b^{3}$
and Maximum value of $a^{6} b^{3}$ is 1 (Using AM, GM).

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