SOLUTION: If the positive integers a and b satisfy √a − √b = √11, what is the maximum value of a/b?

Question 1162750: If the positive integers a and b satisfy √a − √b = √11, what is the maximum value of a/b?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13215) (Show Source): You can put this solution on YOUR website!

The following original response left out important parts of the solution -- though the final answer to the question was correct. See further down for the corrected/expanded response.

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If a and b are integers and , then for some positive integer value of n,

and

Then

For positive integer values of n, the maximum value of a/b is clearly when n=1 and a/b = (2/1)^2 = 4.

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Corrected response....

If a and b are integers and , then for some positive integer value of n,

and

With those values of a and b,

Then

For positive integer values of n, the maximum value of a/b is clearly when n=1 and a/b = (2/1)^2 = 4.

CHECK....

n=1: a = 11(2^2) = 44; b = 11(1^2) = 11; ; a/b = 44/11 = 4

n=2: a = 11(3^2) = 99; b = 11(2^2) = 44; ; a/b = 99/44 = 9/4

n=3: a = 11(4^2) = 176; b = 11(3^2) = 99; ; a/b = 176/99 = 16/9

Clearly for larger values of n the ratio a/b will continue to get smaller....

Answer by ikleyn(52903) (Show Source): You can put this solution on YOUR website!
.

To tutor @greenestamps.

Your assumption that the numbers "a" and "b" are perfect squares, contradicts to the given equation (!)

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