Question -
Answer -
Let the three numbersbe a/r, a, ar
So, according to thequestion
a/r + a + ar = 39/10 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= 39/10
10a + 10ar + 10ar2┬а=39r тАж equation (3)
Substituting a = 1 in3 we get
10(1) + 10(1)r +10(1)r2┬а= 39r
10r2┬атАУ29r + 10 = 0
10r2┬атАУ25r тАУ 4r + 10 = 0тАж equation (4)
5r(2r тАУ 5) тАУ 2(2r тАУ 5)= 0
r = 2/5 or 5/2
so now the equationwill be,
1/(2/5), 1, 1├Ч2/5 or1/(5/2), 1, 1├Ч5/2
5/2, 1, 2/5 or 2/5, 1,5/2
тИ┤┬аThe threenumbers are 2/5, 1, 5/2