Discussion
If a, b, c are real numbers such that \((a - 2)^{2} + (b - 2)^{2} + (c - 2)^{2} = 0\)
Answer: A
a, b, c are in G.P. and \(a + b + c = 6\).
A sum of squares of real numbers is zero only if each square is zero, so \(a = b = c = 2\). Three equal non-zero numbers form a G.P. with common ratio 1 (and also an A.P.), and their sum is 6.
The options with sums 4, 8 or 16 have the wrong total, and 'not in G.P.' is false because a constant non-zero sequence is geometric.
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