anonymous
  • anonymous
The sum of a number and twice another number is 12. What is their maximum product?
Mathematics
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
hello!!! suppose the number be x so the other number will be 2x so according to question x + 2x = 12 3x = 12 x = 4 so 2x = 8 product = 8 * 4 = 32 this the simplest way to solve the problem but maybe its incorrect because of "maximum product".
anonymous
  • anonymous
ChatIndia, you cannot use x + 2x because that would imply they are the same number. It has to be x + 2y. I'm still working on this answer :p
anonymous
  • anonymous
Yea because it says another number!

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anonymous
  • anonymous
nkili, in that case it would be very easy to solve. thanks for the hint
anonymous
  • anonymous
i am sleepy,nkili will solve the problem. :)
anonymous
  • anonymous
I'm really not sure about this one actually haha.... sorry :/
anonymous
  • anonymous
proceed this way (x +2y)^2 = 144
anonymous
  • anonymous
Does anyone disagree with 18?
anonymous
  • anonymous
My answer key says that's the right answer, but how do you solve it.
anonymous
  • anonymous
16
anonymous
  • anonymous
Let x y = k y=k/x Then \[\frac{k}{x}+2 x==12 \] \[\frac{k-12 x+2 x^2}{x}=0 \] Derivative of the Numerator set to 0 then solved for x is x=3 \[\left(\frac{k}{x}+2 x==12\text{/.}x\to 3\right) \text{is}\text{ }\left(6+\frac{k}{3}==12\right) \] k=18
anonymous
  • anonymous
maxima minima trick :P

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