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Q)Thearem ?There ĥ no rational number x such that Proof:We use prool by contradictioheso suppose there are ratonal numbers be the Becaude 0c Ps rational beturen Iand 2 ,and let x smallest one o he Can write where a nd h are 3ntegers.Now let y= xtl oThen y=atb 26 Deyr ralianala The assumption that 2 >l qires a1>2, which implies that yslhe assumption that x >I abo gires s 22) De+uhich implies that y

Q)Thearem ?There ĥ no rational number x such that Proof:We use prool by contradictioheso suppose there are ratonal numbers be the Becaude 0c Ps rational beturen Iand 2 ,and let x smallest one o he Can write where a nd h are 3ntegers.Now let y= xtl oThen y=atb 26 Deyr ralianala The assumption that 2 >l qires a1>2, which implies that yslhe assumption that x >I abo gires s 22) De+uhich implies that y

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Q Thearem :There ů no rational number xsuchtthat Proof: We ube prool by contradictioneso suppose there are rattonal nunmbers be the 2c Îs ratponal betueen Iand 2 ,and let x smallest oneo Can wrte Becaude the where a ond b are Hgers.Now let -Then y=atb Do yu ralianal. The assumption that a >. Which Pmplies that ysl that x>I ires x+l>2. The assumption 22)x+/,which gires implies that But now betwween I and 2 2C oThis contradicti the esthatnAAANDE assumpson that So the theomem Ps torue asing pros by contradiction, a cational oumumberr cohich es smaller than was the smullest one Exphia Pa a few with the po nenences Ohat's
Transcribed Image Text:Q Thearem :There ů no rational number xsuchtthat Proof: We ube prool by contradictioneso suppose there are rattonal nunmbers be the 2c Îs ratponal betueen Iand 2 ,and let x smallest oneo Can wrte Becaude the where a ond b are Hgers.Now let -Then y=atb Do yu ralianal. The assumption that a >. Which Pmplies that ysl that x>I ires x+l>2. The assumption 22)x+/,which gires implies that But now betwween I and 2 2C oThis contradicti the esthatnAAANDE assumpson that So the theomem Ps torue asing pros by contradiction, a cational oumumberr cohich es smaller than was the smullest one Exphia Pa a few with the po nenences Ohat's
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