Question

a² + b² + c² = 35, a + b + c = 9 ∴ ab + bc + ac = ______.

Options

• 15

• 20

• 23

• 25

Answer 1

a² + b² + c² = 35, a + b + c = 9 ∴ ab + bc + ac = 23.

Explanation:

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

(9)² = 35 + 2(ab + bc + ac)

81 = 35 + 2(ab + bc + ac)

2(ab + bc + ac) = 81 − 35

2(ab + bc + ac) = 46

∴ ab + bc + ac = `46/2`

∴ ab + bc + ac = 23