SOLUTION: Two positive numbers differ by 11, and their square roots differ by 1. Find the numbers

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Question 242050: Two positive numbers differ by 11, and their square roots differ by 1. Find the numbers
Answer by solver91311(24713) About Me  (Show Source):
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Let represent the larger of the two positive numbers. Let represent the smaller.

We know their difference is 11, so:



We know the difference of their square roots is 1, so:



Add to both sides of the second equation:



Square both sides



Substitute this value for into the first equation:



Simplify:



And solve:





is a positive number, so so far, so good. Substitute this value into the first equation:





Check:





John