Answers

2016-04-03T14:02:29+05:30
Let the three numbers of GP be a÷r, a, ar
Product of the three numbers is 343.

a÷r × a × ar =343
a3 = 343
a = 3√343
a = 7

Sum of the three numbers is 57

a÷r + a + ar = 57
a[1÷r + 1 + r]= 57
7(1÷r + r÷r + r2÷r)= 57
7+7r+7r2 =57r
7r2-50r+7=0
(r-7)(7r-1)=0
r=7 (or) r=1\7

Case 1:
If r=1\7,the three numbers are,
7(7), 7, 7(1\7)
49, 7 , 1.

Case 2:
If r= 7,the three numbers are,
7(1\7), 7, 7(7)
1, 7, 49.
1 3 1