Question

Arithmetic mean of two positive numbers be $3$ and geometric mean of that two numbers be $2$. Then find the difference of the two numbers.

Answer 1

Let the positive numbers be $a,b$.

Then according to the problem,

$\frac{a+b}{2}=3$

or, $a+b=12$.....(1).

Also,

$\sqrt{ab}=2$

or, $ab=4$......(2).

Now,

$(a-b{)}^2$

$=(a+b{)}^2-4ab$

$=6^2-4\times 4$ [ Using (1) and (2)]

$=20$.

Now, $a-b=\sqrt{20}$.