Question 1108469
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I will denote z = {{{sqrt(lambda)}}}, 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/y}}};  {{{-x/y}}}  is rational;  hence, z is rational.  Contradiction.

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


These contradictions prove the statement.
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