Given:
sum of the numbers = - 3
Product of the numbers = 8
Find:
sum of squares of the numbers
Solution:
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,
- a - d = - 1 - 3 = - 4
- a = - 1
- a + d = - 1 + 3 = 2
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.