Question

The product of three numbers in $G.P.$ is $125$ and sum of their products taken in pairs is $87\frac{1}{2}$. Find them.

Answer 1

Here as above $a=5$.
Also $a^2(r.1+1.\frac{1}{r}+r.\frac{1}{r})=\frac{175}{2}$
or $25(r^2+r+1)=\frac{175}{2}r$
or $2(r^2+r+1)=7r$
or $2r^2-5r+2=0$ or $(r-2)(2r-1)=0$
$\therefore r=2,\frac{1}{2}$.Hence the numbers are
$10,5,5/2$ or $5/2,5,10$.