若a,b,c,d為實數，且a+b√2=c+d√2,則a=b且c=d. 哪裡錯？

Sol
題目改為
若a，b，c，d為實數，且a+b√2=c+d√2，則a=c且b=d 哪裡錯？
令a=√2，b=√2，c=2，d=1
=>
a+b√2=√2+2
c+d√2=2+√2

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若a，b，c，d為有理數就成立

a + b sqrt 2 = c + d sqrt 2
sqrt 2 ( b - d) = c - a
sqrt 2 = c - a/(b - d)
If a = b and c = d, then
sqrt 2 = c - a/(a - c) = -1 !