Question

If a + b + c = 18 and a² + b² + c² = 116 calculate the value of ab + bc + ca
1. 104
2. 108
3. 110
4. 112

Answer 1

Correct Answer - Option 1 : 104

Given

a + b + c = 18

a2 + b2 + c2 = 116

Formula\Concept used

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

Calculation

Clearly,

⇒ 18² = 116 + 2(ab + bc + ca)

⇒ 2(ab + bc + ca) = 208

⇒ ab + bc + ca = 104