If a+b+c =0 and a²+b²+c² =16, find the value of ab + bc + ca.
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Given : a + b + c = 0 and a² + b² + c² = 16
On Squaring both sides, (a + b + c)² = 0²
a² + b² + c² + 2(ab + bc + ca) = 0
[By using an identity (a + b + c)² = a² + b² + c² + 2ab + 2 bc + 2 ca)]
16 + 2(ab + bc + c) = 0
2(ab + bc + ca) = -16
ab + bc + ca = -16/2
ab + bc + ca = - 8
Hence, the value of ab + bc + ca is - 8.
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Answer:
Step-by-step explanation:
[By using an identity (a + b + c)² = a² + b² + c² + 2ab + 2 bc + 2 ca)]
16 + 2(ab + bc + c) = 0
2(ab + bc + ca) = -16
ab + bc + ca = -16/2
ab + bc + ca = - 8
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