If (a + b + c) = 19, and (a2 + b2 + c2) = 155, find the value of (a - b)2 + (b - c)2 + (c - a)2.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 104.
Given that
If (a + b + c) = 19, and (a2 + b2 + c2) = 155
Formula used
a2 + b 2 + c 2 = ( a + b + c ) 2 - 2 (ab + bc + ca)
(a - b)2 + (b - c)2 + (c - a)2 = 2 (a2 + b 2 + c 2) - 2 (ab + bc + ca)
Calculation
⇒ 155 = 192 - 2 × ( ab + bc + ca )
⇒ 2 × ( ab + bc + ca ) = 361 - 155 = 206
As we know,
⇒ (a - b)2 + (b - c)2 + (c - a)2 = 2 × 155 - 206 = 310 - 206 = 104