SOLUTION: Given that x and y are integers and {{{ sqrt( 2sqrt( 10 ) + 11 ) = x + sqrt( x + y ) }}}, find x - y.
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Question 1189763: Given that x and y are integers and , find x - y.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52788) (Show Source): You can put this solution on YOUR website!
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I just solved it yesterday. See the link
https://www.algebra.com/algebra/homework/equations/Equations.faq.question.1189716.html
https://www.algebra.com/algebra/homework/equations/Equations.faq.question.1189716.html
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
Consider the general expansion
You can use that pattern to attempt to find the value of an expression of the form
In this problem, the expression under the radical on the left is
or
According to the pattern above, we should have , , and .
And those are all satisfied when a=1 and b=10. So
Replacing the left side of the given equation with that gives us
Solving by equating the rational and irrational parts of the two expressions gives us x=1 and y=9; so then
ANSWER: x-y = -8
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