## Find positive numbers x and y satisfying the equation xy=12 such that the sum 2x+y is as small as possible.

Question

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## Answers ( No )

We are given equations as

Firstly, we will solve for y

now, we are given sum as

now, we can plug back y

Since, we have to minimize it

so, we will find it’s derivative

now, we can set it to 0

and then we can solve for x

Since , both numbers are positive

so, we will only consider positive value

now, we can find y-value

So, two positive numbers are

…………AnswerAnswer:The positive numbers are .

Explanation:The equation is derived as,

Further simplified as,

Since we have only one local minimum on our open interval it’s the absolute minimum.

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