Multiple choice general knowledge math & puzzles

If a2 + 10b2 + c2 = 2b(3a + c), then which of the following is true? I. a = 3b II. a = b / 3 III. c = b IV. c = 3b V. c = a VI. c = a / 3

  1. Only I

  2. Only II

  3. Only III

  4. I, III and VI

  5. II, IV and V
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Rearranging: a² + 10b² + c² - 6ab - 2bc = 0. This factors as (a-3b)² + (b-c)² = 0. For sum of squares to be zero, each term must be zero: a - 3b = 0 (so a = 3b), and b - c = 0 (so c = b). From these: c = a/3. Statements I, III, and VI are true. Option D is correct.

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