Find the value of ab + bc + ca, when a² + b² + c² = 12 and a + b + c = 5?

13/2

9/2

17/2

None of these

Given:

a² + b² + c² = 12

a + b + c = 5

We know that:

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

Expanding the equation:

5² = 12 + 2(ab + bc + ca)

25 = 12 + 2(ab + bc + ca)

Subtract 12 from both sides:

13 = 2(ab + bc + ca)

Divide by 2:

ab + bc + ca = 13/2