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SMO 2013 Senior Round 1 Question 15

SMO · SMO 2013 Senior Round 1

Question 15

Given that $\sqrt[3]{17-\frac{27}{4}\sqrt6}$ and $\sqrt[3]{17+\frac{27}{4}\sqrt6}$ are the roots of the equation

$$x^2-ax+b=0,$$

find $ab$.