Question

Find three numbers in G.P. whose sum is $13$ & sum of those squares is $91$?

Answer 1

solution -

G.P. $\to a,ar,a{r}^2$

$a+ar+a{r}^2=13$

$a(1+r+r^2)=13.$ __ (1)

Also, $a^2+a^2{r}^2+a^2{r}^4=91$ __ (2)

up on solving

we get a = 1, r = 3

Numbers $\to 1,1\times 3,1\times 3\times 3$

$\Rightarrow 1,3,9.$