Find the value of a² + b² + c², when a + b + c = 9 and ab + bc + ca = 20?
- 61
- 51
- 41
- None of these
Explanation
Given a + b + c = 9 and ab + bc + ca = 20
We know that (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
Substituting the given values:
(9)² = a² + b² + c² + 2(20)
81 = a² + b² + c² + 40
Now, find a² + b² + c²:
a² + b² + c² = 81 - 40
= 41
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