Question

The sum of the squares of three numbers is 83, while sum of their products taken two at a time is 71. Their sum will be
1. 15
2. 49
3. 142
4. 225

Answer 1

Correct Answer - Option 1 : 15

Given:

The sum of the squares of three numbers = 83

The  sum of their products taken two at a time = 71

Calculations:

Let three numbers be 'a', 'b', and 'c'

The sum of the squares of a, b, and c = a² + b² + c²

⇒ a2 + b2 + c2

The sum of their products taken two at a time = ab + bc + ca

⇒ ab + bc + ca = 71

We know that,

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

⇒ (a + b + c)² = 83 + 2 × 71

⇒ (a + b + c)2 = 83 + 142

⇒ (a + b + c)2 = 225

⇒ (a + b + c)2 = 15²

a + b + c = 15     (∵ a^m = b^m  then, a = b)

∴ The sum of three number is 15