If A.M. of two numbers is $15/2$ and their G.M. is $6$, then find the two numbers.
🎥 Video solution / Text Solution of this question is given below:
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.