Let the numbers be a and b. Given that the product of the numbers is 3600.
ab = 3600
We can use the AM-GM Inequality here to solve the problem. The arithmetic mean-geometric mean (AM-GM) inequality states that the arithmetic mean of positive real numbers is greater than or equal to the geometric mean of the numbers.
Let a and b are positive numbers, arithmetic mean is greater than or equal to geometric mean.
AM-GM Inequality states that:
or more in general for n numbers the equation states that :
Now to answer the question : we known the product ab = 3600.
replace the product of the two numbers in the equation
Square root of 3600 is 60. So we get
Hence the minimum value of the sum of the numbers is 120.
Proof for the AM-GM equation for two numbers:
Square both sides, we get
Expand and rearrange the terms, we get:
This equation holds true, since square of a number is always positive i.e
Let y = a-b