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Question 975125: Give an example of two irration number whose sum is rational number
Found 3 solutions by farohw, solver91311, Alan3354:
Answer by farohw(175)   (Show Source):
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website!
Begin with
We must first demonstrate that  is irrational. Assume that is rational. We know that the sum of two rational numbers is rational (proof on request), so ) must be rational. But  , which means that  must be rational. However, we know that not to be the case, hence we have contradicted our original assumption that is rational. Therefore is, in fact, irrational.
In a similar fashion, we can demonstrate that  is also irrational. However, the sum:
\ +\ (1\ -\ \sqrt{2})\ =\ 2)
is rational, answering the question posed.
Demonstrate that the product of these two irrational numbers is rational. Proof left as an exercise for the student. Hint: remember the factorization of the difference of two squares.
John
My calculator said it, I believe it, that settles it
Answer by Alan3354(69443)  (Show Source):
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