Question

The sum of three numbers is 30 and their product 750. What are the three numbers?

(a) -2, -6 and -10

(b) 2, 6, and 10

(c) 5, 10 and 15

(d) -5, -10 and -15

The question was posed to me in homework.

I would like to ask this question from Arithmetic Progression Basics in portion Arithmetic Progressions of Mathematics – Class 10

Answer 1

Right answer is (c) 5, 10 and 15

For explanation: Let the three numbers in AP be (a + d), a, and (a – d).

Sum of the five numbers is 30.

∴ (a + d) + a + (a – d) = 30

3a = 30

a = 10

Now, product of the numbers is 750.

∴ (a + d)a(a – d) = 750

a^3 – d^2 a = 750

Substituting a = 10, we get

10^3 – d^2 (10) = 750

1000 – d^2 (10) = 750

250 = 10d^2

d^2 = 25

d = 5, -5

The three numbers are 5, 10 and 15.