If a + b + c = 9 (where a, b, c are real numbers), then

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If a + b + c = 9 (where a, b, c are real numbers), then the minimum value of a² + b² + c² is

a + b + c = 9
a² + b² + c²
= (a + b + c)² – 2 (ab + bc + ca)
[ab + bc + ca will be maximum if a = b = c]
a² + b² + c² = 9² – 2 × 27
= 81 – 54 = 27