Find two positive integers greater than one whose product is 24,999,999 and whose positive difference is as large as possible.

Now, I understand that the positive integers could be 124,999,99.5. It's the rest of the problem that confuses me.

Question

Find two positive integers greater than one whose product is 24,999,999 and whose positive difference is as large as possible. 

Now, I understand that the positive integers could be 124,999,99.5. It's the rest of the problem that confuses me.

anonymous · Answer

Oh-and medals for the correct answer!

amistre64 · Answer

xy >k

x-y = max ??

amistre64 · Answer

either way you will have to solve a quadratic

amistre64 · Answer

if xy = k,  then we can sub in y = k/x

f(x) = x - k/x  is max when f' = 0

anonymous · Answer

What is a quadratic?

anonymous · Answer

I don't understand what your saying, sorry. :(

amistre64 · Answer

its a poly of degree 2,  but that might be a stray thought ...

amistre64 · Answer

let y = k/x

therefore:  f(x) = x - k/x

f' = 1 + k/x^2 = 0

x^2 + k = 0

x = sqrt(k)  seems like a good bound

amistre64 · Answer

sqrt(24999999) is about 4999.999....

so let x = 4999 and y= 24999999/x = 5001

anonymous · Answer

I have to eat dinner sorry...

anonymous · Answer

So the answer is 5001?

amistre64 · Answer

positive difference is as large as possible

i think i found the "as small as possible" instead

amistre64 · Answer

1 and 24 999 999 might be the max positive difference

amistre64 · Answer

Find two positive integers greater than one whose product is 24,999,999 and whose positive difference is as large as possible. 

since the product of 1 and 24 999 999 is equal to 24 999 999; and the difference between them is 24 999 998

i would say that you are looking for x=1 and y = something approaching infinity .....