Question

The middle of the three numbers is continued proportion is 15 and the sum of the first and third is 34, find the numbers?​

Answer 1

Let the numbers be x, y, z.

As the numbers are in continued proportion, therefore

y2 = xz ……………… (1)

Also, the mean proportion = 12

∴ y = √xz = 15

⇒ xz = 225…………… (2)

It is given that the sum of remaining two numbers = 34

∴ x + z = 34

⇒ x = 34 – z

Put the value of x in equation (2):

(34– z)z = 225

⇒ 34z – z2 = 225

⇒ z2 – 34z + 225= 0

⇒ z2 – 25z – 9z + 225 = 0

⇒ z(z - 25) -9(z-25) = 0

⇒ (z - 9)(z - 25) = 0

⇒ z = 9or z = 25

∴ x = 34 – 9or x = 34– 25

⇒ x = 25or x = 9.

y=15