If (a + b + c) = 20 and a2 + b2 + c2 = 262 then, find the value of ab+ bc + ca
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 69.
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
⇒ (20)2 = 262 + 2(ab + bc + ca)
⇒ 2(ab + bc + ca) = 202 - 262 = 400 - 262 = 138
⇒ (ab + bc + ca) = 138/2 = 69
Therefore, the value of ab + bc + ca is 69.