SOLUTION: (a+b square root 2) (a-b square root 2)
Prove that this is an integer a,b are integers
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Question 978538: (a+b square root 2) (a-b square root 2)
Prove that this is an integer a,b are integers
Found 2 solutions by josgarithmetic, solver91311:
Answer by josgarithmetic(39838) (Show Source): You can put this solution on YOUR website!
Subtraction of integers will have element of the set of integers.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
\left(a\ -\ b\sqrt{2}\right))
Is the product of two conjugates. The product of two conjugates is the difference of two squares.
^2\ =\ 2)
by definition of square root, and 
by definition of Integer.
,
,
and
by Closure of Integer Multiplication.
by Closure of Integer Subtraction.
Q.E.D.
John
My calculator said it, I believe it, that settles it
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