2014 Singapore MO (Junior Rd 1) Problem 32

2014 SMO (Junior-Rd1) 32. For a \geq \frac{1}{8}, we define

g(a) = \sqrt[3]{a + \displaystyle\frac{a+1}{3}\sqrt{\frac{8a-1}{3}}} +\sqrt[3]{a - \displaystyle\frac{a+1}{3}\sqrt{\frac{8a-1}{3}}}.

Find the maximum value of g(a).

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