SOLUTION: One pair of integers (x,y) solves {{{sqrt(4sqrt(7) + 11) = y + sqrt(x)}}}. Find x.y

Algebra ->  Finance -> SOLUTION: One pair of integers (x,y) solves {{{sqrt(4sqrt(7) + 11) = y + sqrt(x)}}}. Find x.y      Log On


   

Question 1105658: One pair of integers (x,y) solves sqrt%284sqrt%287%29+%2B+11%29+=+y+%2B+sqrt%28x%29. Find x.y
Answer by Edwin McCravy(20066) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%284sqrt%287%29+%2B+11%29+=+y+%2B+sqrt%28x%29

Square both sides:

%28sqrt%284sqrt%287%29+%2B+11%29%29%5E2+=+%28y+%2B+sqrt%28x%29%29%5E2

4sqrt%287%29+%2B+11+=+%28y+%2B+sqrt%28x%29%29%28y+%2B+sqrt%28x%29%29

"FOIL" out the right side:

4sqrt%287%29+%2B+11+=+y%5E2+%2B+y%2Asqrt%28x%29%2By%2Asqrt%28x%29%2B%28sqrt%28x%29%29%5E2

4sqrt%287%29+%2B+11+=+y%5E2+%2B+2y%2Asqrt%28x%29%2Bx

Since we know that one pair of integers (x,y) solves it,
the terms with the square roots on each side must be equal, 
and therefore the terms without square roots must also be equal.
So we have this system of equations

system%284sqrt%287%29=2y%2Asqrt%28x%29%2C11=y%5E2%2Bx%29

I'll let you finish.  

Divide both sides of the first equation
by 2, then square both sides.
Solve it for either x or y2
Substitute what you get into the second equation  
Solve for that letter.
Substitute to find the other letter.

Edwin