Question
If a2 + b2 + c2 = 20 and a + b + c = 0, find ab + bc + ca.
✓
Answer
Recall the formula
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
Given that
a2 + b2 + c2 = 20
(a + b + c) = 0
Then we have
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
(0)2 = 20 + 2(ab + bc + ca)
20 + 2(ab + bc + ca) = 0
2(ab + bc + ca) = -20
(ab + bc + ca) = -10
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
Given that
a2 + b2 + c2 = 20
(a + b + c) = 0
Then we have
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
(0)2 = 20 + 2(ab + bc + ca)
20 + 2(ab + bc + ca) = 0
2(ab + bc + ca) = -20
(ab + bc + ca) = -10
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