Question

If (a + b + c) = 17, and (a² + b² + c²) = 101, find the value of (a - b)² + (b - c)² + (c - a)².

• A. 12
• B. 14
• C. 10
• D. 16

Answer 1

Answer:

B. 14

Solution:

Given:

(a + b + c) = 17, and (a² + b² + c²) = 101

Formula used:

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

Calculation:

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

⇒ 17² = 101 + 2 (ab + bc +ca)

⇒  (ab + bc +ca) = 94

 (a - b)² + (b - c)² + (c - a)².

⇒ 2 (a² + b² + c²) - 2 (ab + bc +ca)

⇒  $101\times{2}-2\times{94}=14$