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 the largest of those numbers ?

Answer 1

Let the numbers in G.P are, $\frac{a}{r},a,ar$
$\Rightarrow a=5$
Also, $a^2(\frac{1}{r}.1+1.r+r.\frac{1}{r})=\frac{175}{2}$
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 $5/2,5,10$