Find the value of ab + bc + ca, when a² + b² + c² = 12 and a + b + c = 5?
- 13/2
- 9/2
- 17/2
- None of these
Explanation
Given:
a² + b² + c² = 12
a + b + c = 5
We know that:
(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
Expanding the equation:
5² = 12 + 2(ab + bc + ca)
25 = 12 + 2(ab + bc + ca)
Subtract 12 from both sides:
13 = 2(ab + bc + ca)
Divide by 2:
ab + bc + ca = 13/2
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