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Agentjamesbond007
 4 years ago
Find two positive numbers whose product is 100 and whose sum is a minimum.
[please explain how to solve]
Agentjamesbond007
 4 years ago
Find two positive numbers whose product is 100 and whose sum is a minimum. [please explain how to solve]

This Question is Closed

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.0\[xy=100\] let's call the Sum S S=x+y

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.0now solve xy=100 for either x or y

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0xy = 100 or y = 100/x and we need to minimize F = x + y = x + 100/x now we are ready to take the derivative of F.

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.0\[Sum=x+\frac{100}{x}\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0You can find the minimum of x + (100/x) using only Algebra 2 or Geometry if you're Calculusimpaired.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Noooooo derivativeee pleaseeeeee!!!

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Simple inequalities would do just fine.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Set S equal to the sum, x+(100/x), and solve that equation for x in terms of S. You'll get a parabola in x that has only one minimum at the Vertex of that parabola.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0If the product of the two variables is constant, the sum of the two variables will be least when they are equal.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0@FoolForMath: but how to prove that rigorously without calculus / derivatives?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0@Broken Fixer:AMGM inequality.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0@Luis: if Sum = 100 then there is no way to attain the minimum product with positive reals (infimum is 0).
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