If the sum of three numbers in G.P. is 63 and the product of the first and the second term is 34of the third term, then the numbers are

Let the three numbers be a, ar,ar2Given a+ar+ar2=63-------------- (1)and a⋅ar=34⋅ar2 or a=34r------------------(2)putting in  (1)   34r+34r⋅r+34r⋅r2=63or          r3+r2+r−84=0 or  (r−4)r2+5r+21=0∴ r=4,−5±25−842∴ Real value of r is 4. Putting this value in (2),   a=34×4=3∴The three numbers are 3,3×4,3×42,i e  3, 12, 48.