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) About Me  (Show Source):
You can put this solution on YOUR website!
a%5E2-b%5E2%2A2
Subtraction of integers will have element of the set of integers.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




Is the product of two conjugates. The product of two conjugates is the difference of two squares.



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