The product of two positive real numbers is 20. Find the least possible sum of two such real numbers

Question

anonymous · Answer

9 is the least possible sum the 2 nums r 4 and 5 if Im right ;)

anonymous · Answer

@sneakergyrl is right if the numbers should be distinct otherwise the numbers would be $$2\sqrt{5}$$ and $$2\sqrt{5}$$
And the least sum would be $$4\sqrt{5}$$

anonymous · Answer

I think you should go with 4 and 5.

anonymous · Answer

do you know how to solve it using calculus?

anonymous · Answer

thanks @ShailKumar

anonymous · Answer

So, if the numbers be x and y, then x*y = 20.
We want to minimize, s = x+y
So, s = x+20/x
Now find ds/dx and put it equal to zero to solve for x.

anonymous · Answer

So would you have 1+20/x^2=0?

anonymous · Answer

No

anonymous · Answer

1-20/x^2=0

anonymous · Answer

can you have a square root for your answer?

anonymous · Answer

Yes, you are getting x = 2 sqr root 5, which is a real number.

anonymous · Answer

Thank you!