Answer:
The two positive numbers whose product is 81 and whose sum is a minimum are 9 and 9.
Step-by-step explanation:
81 is divisible by 1 and 81, since 81/1 = 81 and 81/81 = 1.
81 is divisible by 3 and 27, since 81/3 = 27 and 81/27 = 3.
81 is divisible by 9, since 81/9 = 9.
Their sums are.
81 + 1 = 82.
3 + 27 = 30
9 + 9 = 18.
So the two positive numbers whose product is 81 and whose sum is a minimum are 9 and 9.
Answer:
The two positive numbers will be 9 and 9.
Step-by-step explanation:
Let the two positive numbers be x and y.
It is given that the product of the number is 81 the sum of them is minimum.
So, the product can be written as [tex]xy=81[/tex].
The sum can be written as [tex]x+y=x+\dfrac{81}{x}[/tex]. It is required to minimize the sum.
Differentiate the sum as,
[tex]x+y=x+\dfrac{81}{x}\\1+y'=1-\dfrac{81}{x^2}=0\\x^2=81\\x=9\\y=\dfrac{81}{x}\\y=9[/tex]
Now, the second derivative of the sum will be,
[tex]y''=2\times \dfrac{81}{x^3}>0[/tex]
So, the second derivative is positive and hence, the sum will be minimum at x=9.
Therefore, the two positive numbers will be 9 and 9.
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https://brainly.com/question/21797759?referrer=searchResults
