SOLUTION: two positive numbers differ by 11, and their square roots differ by 1. Find the numbers.
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Question 173445: two positive numbers differ by 11, and their square roots differ by 1. Find the numbers.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Let's go at this straight up and see what happens:
Let one of the numbers be and the other one be , so we know that:
and .
Yuck! You can see right off that those radicals are going to make this messy.
So let's try another tack.
Let's keep and as the desired variables, but let's define two more variables, thus:
Let and . That means that and .
Now we can write:
1. and
2.
Solve Eq. 2 for , and substitute this expression for in Eq. 1.
Expand the binomial and collect terms:
Since we know that ,
But and
Hence, 36 and 25 are the two numbers.
Check:
Answer checks.
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