Let the three numbers be \( \dfrac{a}{r}\), a, ar

So, according to the question

\( \dfrac{a}{r} + a + ar = 38\) … equation (1)

\( \dfrac{a}{r} + a + ar = 1728\) … equation (2)

From equation (2) we get,

a^{3} = 1728

a = 12.

From equation (1) we get,

\(\dfrac{ (a + ar + ar^2)}{r}\) = 38

a + ar + ar^{2} = 38r … equation (3)

Substituting a = 12 in equation (3) we get

12 + 12r + 12r^{2} = 38r

12r^{2} – 26r + 12 = 0… equation (4)

Dividing equation (4) by 2 we get

6r^{2} – 13r + 6 = 0

6r^{2} – 9r – 4r + 6 = 0

3r(3r – 3) – 2(3r – 3) = 0

r = \( \dfrac{3}{2}\)

Now the equation will be

(\( \dfrac{12}{ \dfrac{3}{2}}\)) = 8 or

So the terms are 8, 12, 18

The three numbers are 8, 12, 18

Answered by Sakshi | 1 year agoConstruct a quadratic in x such that A.M. of its roots is A and G.M. is G.

Find the geometric means of the following pairs of numbers:

**(i) **2 and 8

**(ii) **a^{3}b and ab^{3}

**(iii) **–8 and –2

Insert 5 geometric means between \( \dfrac{32}{9}\) and \( \dfrac{81}{2}\).