Question

pls tell me tgis qies with brief explanation . it is related to gp

Answer 1

The numbers are 2/5, 1, 5/2.
Let's go through this step by step.

Answer 2

Let the three numbers in GP be (a/r), a, ar.

(i)

Sum of three numbers in G.P is (39/10).

⇒ (a/r) + a + ar = 39/10

(ii)

Given that product of three numbers is 1.

⇒ (a/r) * (a) * (ar) = 1

⇒ a^3 = 1

⇒ a = ∛1

⇒ a = 1.

Substitute a = 1 in (i), we get

⇒ (a/r) + a + ar = 39/10

⇒ (1/r) + 1 + r = 39/10

⇒ 1 + r + r^2 = (39/10) * r

⇒ (10 + 10r + 10r^2) = 39r

⇒ 10 + 10r + 10r^2 - 39r = 0

⇒ 10r^2 - 29r + 10 = 0

⇒ 10r^2 - 25r - 4r + 10 = 0

⇒ 5r(2r - 5) - 2(2r - 5) = 0

⇒ (2r - 5)(5r - 2) = 0

⇒ r = (2/5), (5/2).

Now,

When r = 2/5:

(i) a/r = 5/2

(ii) a = 1

(iii) ar = 2/5.

When r = 5/2:

(i) a/r = 2/5

(ii) a = 1

(iii) ar = 5/2.

Therefore, the numbers are 2/5, 1, 5/2 (or) 5/2, 1, 2/5.

Hope it helps!