If a + b + c = 10 and a2 + b2 + c2 = 48, then the value of ab + bc + ca is _______.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 26.
We know that,
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
Now, according to the question
Using the formula (a + b + c)2 we get,
⇒ (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
⇒ (10)2 = 48 + 2(ab + bc + ca)
⇒ 100 - 48 = 2(ab + bc + ca)
⇒ ab + bc + ca = 52/2 = 26
Therefore, the value of ab + bc + ca is 26.