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) About Me  (Show Source):
You can put this solution on YOUR website!
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I will denote z = sqrt%28lambda%29, 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 = -x%2Fy;  -x%2Fy  is rational;  hence, z is rational.  Contradiction.

If x =/= 0,  then from (1)  1%2Fz = -y%2Fx;  -y%2Fx is rational;  hence, 1%2Fz  is rational;  then z is rational   Contradiction.


These contradictions prove the statement.