If $a^2 + b^2 + c^2 = 62 $ and a + b + c = 12, then what is the value of $ 4ab + 4bc + 4ca $ ?
Answer & explanation
Correct answer: option 1
a2 + b2 + c2 = 62
a + b + c = 12
We know that,
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
122 = 62 + 2(ab + bc + ca)
144 = 62 + 2(ab + bc + ca)
82 = 2(ab + bc + ca)
41 = ab + bc + ca
4ab + 4bc + 4ca = 4 × 41 = 164