# Algebra – 2

## 11 thoughts on “Algebra – 2”

1. kingsly |

xy^3 = 64.
find minimum value of x+12y.
i tried the method as above, i get x= 4th root of (64/27)….pls advice

• 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

2. Abhishek Kulkarni |

For the last problem, what will be the maximum value of a+b+c when a^2*b*c^4 = 1024. Please explain ?

• 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

3. Aakash |

4. Sailendra Surla |

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

5. Kishan |

I saw a question on quora. Find max value of 3x + 4y=12.
I got the right answer when I tried with 3x/2 + 3x/2 + 4y/2+4y/2=12 however my answer is wrong when I tried putting 3x/3 + 3x/3 + 3x/3 + 4y/2 + 4y/2 =12. Why is it so? Need help.

• “Find max value of 3x + 4y=12” is an incomplete question. (That value will always be 12!) If you provide the complete question, maybe I can help.

regards
J

• Kishan |

Sorry sir. The question is “Is it possible to find the maximum value of 3x+4y=12? “.It’s clear from your comment that it is not.Can you tell me the reason?

6. That still doesn’t make sense. A valid question could be something like “Find the maximum value of x^2 + y^2 given that 3x + 4y = 12”. Or “Find the maximum value of 3x + 4y given that x^2 + y^2 = 12”.

This question is like asking “find the maximum value of x = 4”. There is nothing to find here as everything is fixed already. Possibly the person who posted it was in a hurry and missed out something.

regards
J