Question

Find the minimum sum of two positive numbers (not necessarily integers) whose product is 150.

Answer 1

Answer:

Step-by-step explanation:

Let 1 number be x and the other number be y

Then x+y = 300

y = 300-x

Now we know that the first differentiation of maxima and minima is equal to 0

So dy/dx = 0

Here y = The product of the two numbers ie x(300-x) as we are given that the product of the 2 numbers corresponds to maxima.

dy/dx = d/dx x(300-x)

= d/dx (300x-x^2)

Applying the following rules

x^n = nx^n-1*dy/dx (x) and

dy/dx (a-b) = dy/dx (a) - dy/dx (b)

= 300*x^0 [d/dx (x)] - 2*x^1[d/dx (x)]

= 300 - 2x

Now we can equate it to 0

300 - 2x = 0

x = 150

So substituting value of x in the equation x+y = 300

We get value of y also equal to 150

Now you can check the answer too although it will be very lengthy by hit and trial but I guarantee you that you will never get a pair whose product is greater than these.