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Which statement creates the actual contradiction in the proof for (\sqrt{3})?किस कथन से (\sqrt{3}) के प्रमाण में वास्तविक विरोधाभास बनता है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (a) and (b) were assumed coprime, but both turned out divisible by (3)(a) और (b) सहअभाज्य माने गए थे, पर दोनों (3) से विभाज्य निकले
Step 1: In lowest form, numerator and denominator must be coprime. Step 2: The proof forces both to have (3) as a common factor. Step 3: Coprimality and a common factor cannot occur together.चरण 1: सरलतम रूप में अंश और हर सहअभाज्य होने चाहिए। चरण 2: प्रमाण में दोनों में (3) साझा गुणनखंड आ जाता है। चरण 3: सहअभाज्य और साझा गुणनखंड साथ-साथ नहीं हो सकते।
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