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If a + b + c = 0 and a ^ 2 + b ^ 2 + c ^ 2 = 16 find the value of ab + bc + ca?
Most Upvoted Answer
If a + b + c = 0 and a ^ 2 + b ^ 2 + c ^ 2 = 16 find the value of ab +...
Given Information:
a + b + c = 0
a ^ 2 + b ^ 2 + c ^ 2 = 16

Finding ab + bc + ca:
To find the value of ab + bc + ca, we can manipulate the given equations to simplify the expression.

Expanding the Equation:
(a + b + c) ^ 2 = a ^ 2 + b ^ 2 + c ^ 2 + 2(ab + bc + ca)
Substitute the values of a + b + c and a ^ 2 + b ^ 2 + c ^ 2:
0 = 16 + 2(ab + bc + ca)
ab + bc + ca = -8

Final Answer:
The value of ab + bc + ca is -8.
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If a + b + c = 0 and a ^ 2 + b ^ 2 + c ^ 2 = 16 find the value of ab + bc + ca?
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