Question 24

The geometric and arithmetic means of two positive numbers are respectively $$8$$ and $$17$$. The larger of the two numbers is

Correct Answer: 32

Solution

Let the numbers be $$u$$ and $$v$$. Then $$u+v=34$$ and $$uv=64$$, so they are the roots of $$t^2-34t+64=0$$. The roots are $$17\pm\sqrt{17^2-8^2}=17\pm15$$, giving $$32$$ and $$2$$. Hence the larger number is $$32$$.

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