SOLUTION: x=rational and y=rational λ^1/2=irrational and x+y*λ^1/2=0 show that x=o or y=o

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Question 1108469: x=rational and y=rational λ^1/2=irrational and x+y*λ^1/2=0 show that x=o or y=o
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
I will denote z = , for brevity.


We are given that z is irrational, x and y are rational and 


x + y*z = 0.    (1)


If y =/= 0,  then from (1)  z = ;    is rational;  hence, z is rational.  Contradiction.

If x =/= 0,  then from (1)   = ;   is rational;  hence,   is rational;  then z is rational   Contradiction.


These contradictions prove the statement.


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