Question -
Answer -
Let the three numbersbe a/r, a, ar
So, according to thequestion
a/r + a + ar = 13/12 …equation (1)
a/r × a × ar = -1 …equation (2)
From equation (2) weget,
a3 =-1
a = -1
From equation (1) weget,
(a + ar + ar2)/r= 13/12
12a + 12ar + 12ar2 =13r … equation (3)
Substituting a = – 1in equation (3) we get
12( – 1) + 12( – 1)r +12( – 1)r2 = 13r
12r2 +25r + 12 = 0
12r2 +16r + 9r + 12 = 0… equation (4)
4r (3r + 4) + 3(3r +4) = 0
r = -3/4 or r =-4/3
Now the equation willbe
-1/(-3/4), -1, -1×-3/4or -1/(-4/3), -1, -1×-4/3
4/3, -1, ¾ or ¾, -1,4/3
∴ The threenumbers are 4/3, -1, ¾ or ¾, -1, 4/3