Question

The sum of three numbers in AP is - 8 and the product is 1 find the numbers

Answer 1

Given info : the sum of three numbers in arithmetic progression is -8 and the product of these terms is 1.

To find : the numbers

solution : let (a - d), a and (a + d) are three terms in arithmetic progression.

sum of three terms = - 8

⇒(a - d) + a + (a + d) = -8

⇒ 3a = -8

⇒a = -8/3

Now product of terms = 1

⇒(a - d)a(a + d) = 1

⇒(a³ - ad²) = 1

⇒(-8/3)³ - (-8/3)d² = 1

⇒-512/27 + 8d²/3 = 1

⇒8d²/3 = 1 + 512/27 = 539/27

⇒d = ±√(539/72) ≈ ±2.74

therefore the numbers are ;

a - d = -8/3 - 2.74 = -5.406

a = -8/3 = -2.67

a + d = -8/3 + 2.74 = 0.073