Question -
Answer -
Let the three numbersbe a/r, a, ar
So, according to thequestion
a/r + a + ar = 13/12 тАжequation (1)
a/r ├Ч a ├Ч ar = -1 тАжequation (2)
From equation (2) weget,
a3┬а=-1
a = -1
From equation (1) weget,
(a + ar + ar2)/r= 13/12
12a + 12ar + 12ar2┬а=13r тАж equation (3)
Substituting a = тАУ 1in equation (3) we get
12( тАУ 1) + 12( тАУ 1)r +12( тАУ 1)r2┬а= 13r
12r2┬а+25r + 12 = 0
12r2┬а+16r + 9r + 12 = 0тАж equation (4)
4r (3r + 4) + 3(3r +4) = 0
r = -3/4┬аor r =-4/3
Now the equation willbe
-1/(-3/4), -1, -1├Ч-3/4or -1/(-4/3), -1, -1├Ч-4/3
4/3, -1, ┬╛ or ┬╛, -1,4/3
тИ┤┬аThe threenumbers are┬а4/3, -1, ┬╛ or ┬╛, -1, 4/3