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Question 7

$$a, b$$ are natural numbers. If $$9a^2 = 12a + 96$$ and $$b^2 = 2b + 3$$, the value of $$2018(a+b)$$ is

Solution

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From $$3a^2 - 4a - 32 = 0$$ the natural number solution is $$a = 4$$. From $$b^2 - 2b - 3 = 0$$, i.e. $$(b-3)(b+1) = 0$$, the natural number solution is $$b = 3$$. So $$a+b=7$$ and $$2018 \times 7 = 14126$$.

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