Multiple choice general knowledge math & puzzles

find the least value of 3x+4y if x^2y^3=6

  1. 24

  2. 26

  3. 16

  4. 10
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

We need to minimize 3x + 4y given x²y³ = 6. Using AM-GM inequality or Lagrange multipliers, we can rewrite as (3x/2) + (3x/2) + (4y/3) + (4y/3) + (4y/3) ≥ 5×[(3x/2)²(4y/3)³]^(1/5) = 5×[(9x²/4)(64y³/27)]^(1/5) = 5×[(576x²y³/108)]^(1/5) = 5×[(16×6/3)]^(1/5) = 10. Equality occurs when all terms are equal.

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