Question

If the continued product of three numbers in G.P. is 216 and the sum of the products taken in pairs is 156, find the biggest number among the three numbers.

Answer 1

Since the continuous product of three numbers is $216$, the numbers will be of the form $\frac{6}{a},6,6a$.
Now the sum of products taken in pairs is $156$.
$\Rightarrow 36a+\frac{36}{a}+36=156$
$\Rightarrow a+\frac{1}{a}=\frac{120}{36}$
$\Rightarrow a+\frac{1}{a}=\frac{10}{3}$
$\Rightarrow a=3$
The numbers are thus $2,6$ and $18$.