The sum of 3 terms in A. P. is - 3 and their product is 8, then sum of squares of the numbers is

sum of the numbers = - 3

Product of the numbers = 8

sum of squares of the numbers

Let the three terms be a - d , a , a + d.

sum of the numbers = - 3

→ a - d + a + a + d = - 3

→ 3a = - 3

→ a = - 3/3

→ a = - 1

Also,

Product of the numbers = 8

→ (a - d) * (a) * (a + d) = 8

Putting the value of a and using (a + b) * (a - b) = a² - b² we get,

→ [ (- 1)² - d² ] = 8/ - 1

→ 1 - d² = - 8

→ 1 + 8 = d²

→ 9 = d²

→ d = 3

Hence,

Now,

Finding Sum of their squares :

→ (a - d)² + a² + (a + d)²

→ ( - 4)² + ( - 1)² + (2)²

→ 16 + 1 + 4

→ 21

Hence, the sum of the squares of the three terms is 21.

I hope it will help you.

Regards.

b. astronomers