if a^2+b^2+c^2=20 and a+b+c = 0 find ab+bc+ca
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Answer:
- 10
Step-by-step explanation:
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
Therefore, ab + bc + ca = -10
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