Question -
Answer -
Let the three numbersbe a/r, a, ar
So, according to thequestion
a/r × a × ar = 125 …equation (1)
From equation (1) weget,
a3 =125
a = 5
a/r × a + a × ar + ar× a/r = 87 ½
a/r × a + a × ar + ar× a/r = 195/2
a2/r + a2r+ a2 = 195/2
a2 (1/r+ r + 1) = 195/2
Substituting a = 5 inabove equation we get,
52 [(1+r2+r)/r]= 195/2
1+r2+r = (195r/2×25)
2(1+r2+r) =39r/5
10 + 10r2 +10r = 39r
10r2 –29r + 10 = 0
10r2 –25r – 4r + 10 = 0
5r(2r-5) – 2(2r-5) = 0
r = 5/2, 2/5
So G.P is 10, 5, 5/2or 5/2, 5, 10
∴ The threenumbers are 10, 5, 5/2 or 5/2, 5, 10