Question

If (a + b + c) = 8 and a² + b² + c² = 40 then find (ab + bc + ca).

1. 4
2. 8
3. 12
4. 24

Answer 1

Correct Answer - Option 3 : 12

Given:

(a + b + c) = 8

a² + b² + c² = 40

Formula used:

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

Calculations:

Using the given values,

⇒ 8² = 40 + 2(ab + bc + ca)

⇒ 64 = 40 + 2(ab + bc + ca)

⇒ 24 = 2(ab + bc + ca)

⇒ (ab + bc + ca) = 12

∴ ab + bc + ca = 12