7 thoughts on “Algebra – 2

    • Kingsly, here you would have to say since we want y^3, let’s split 12y as 4y + 4y + 4y. So we need x = 4y so 4y * y^3 = 64 so y = 2 and x = 8 and so x + 12y = 32 I would guess…

      regards
      J

    • There won’t be a maximum limit, Abhishek. If we make a and b very small (close to zero), then c will become very large (tending to infinity) and so the total will tend to infinity as well. Remember that we are talking positive real numbers here and not integers.

      regards
      J

  1. If 2x+y =8, maximum value of x^4 * y^3, Solved it by taking 2x/4 =y/3 which implies, taking value of x =2 and y =3 so maximum is 2^4 * 3^3 but answer is given to be as 2^18 * 3^3. the answer was explained in A.M>= G.M approach. could you please explain the flaw in my logic.

    • Neither answer seems correct. If we don’t have a condition on x and y, then it can go to infinity. If we restrict x and y to be positive, even then the max will come when x = 16/7 and y = 24/7. You have assumed x and y to be natural numbers I guess, but I see no reason for that in the question.

      Do double-check the question; the answer 2^18*3^3 would come if the question was 2x+y = 28. Perhaps you have read it incorrectly or else there is a typo in the question….

      regards
      J

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