Asked by Ahmed
Find two positive numbers whose product is 81 and whose sum is a minimum. (If both values are the same number, enter it into both blanks.)
Answers
Answered by
oobleck
9,9
a square has minimum perimeter for a given area
a square has minimum perimeter for a given area
Answered by
mathhelper
let one number be x, then the other is 81/x
sum = x + 81/x
d(sum)/dx = 1 - 81/x^2
= 0 for a min
1 = 81/x^2
x^2 = 81
x = 9 , since x must be positive
so if one is 9, the other is 81/9 which is also 9
sum = x + 81/x
d(sum)/dx = 1 - 81/x^2
= 0 for a min
1 = 81/x^2
x^2 = 81
x = 9 , since x must be positive
so if one is 9, the other is 81/9 which is also 9
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