document.write( "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 \n" ); document.write( "

Algebra.Com's Answer #723467 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "I will denote z = , for brevity.\r\n" );
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document.write( "We are given that z is irrational, x and y are rational and \r\n" );
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document.write( "x + y*z = 0.    (1)\r\n" );
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document.write( "If y =/= 0,  then from (1)  z = ;    is rational;  hence, z is rational.  Contradiction.\r\n" );
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document.write( "If x =/= 0,  then from (1)   = ;   is rational;  hence,   is rational;  then z is rational   Contradiction.\r\n" );
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document.write( "These contradictions prove the statement.\r\n" );
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