The product of the three numbers in G.P. is 125 and sum of their product taken in pairs is `(175)/2` . Find them.

Answer

5/2, 5,11

Explanation

Let three terms in G.P. be a/r,a,ar. Given that the product is 125.
`therefore` a=5
Also, `a^(2)(rxx1+1xx1/r+rxx1/r)=175/2`
or `25(r^(2)+r+1)=175/2r`
or `2(r^(2)+r+1)=7r`
or `2r^(2)-5r+2=0`
or `(r-2)(2r-1)=0`
or `r=2,1/2`
Hence, the numbers are 10,5,5/2 or 5/2,5,10.