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Previous Year Question (PYQs)

If A.M. of two numbers is $15/2$ and their G.M. is $6$, then find the two numbers.




Solution

Let the numbers be $a$ and $b$. $\dfrac{a + b}{2} = \dfrac{15}{2} \Rightarrow a + b = 15$ and $\sqrt{ab} = 6 \Rightarrow ab = 36$ Now, $a$ and $b$ are roots of $x^2 - 15x + 36 = 0$ $\Rightarrow x = 12, 3$ Hence, the numbers are 12 and 3.

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