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In which situation is the rational assumption for (\sqrt{2}) proved false?किस स्थिति में (\sqrt{2}) की परिमेय मान्यता गलत सिद्ध हो जाती है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: When (p) and (q) in lowest form are both proved evenजब सरलतम रूप के (p) और (q) दोनों सम सिद्ध हों
Step 1: In lowest form, (p) and (q) should be coprime. Step 2: If both are proved even, both have common factor (2). Step 3: This is impossible, so the rational assumption is false.चरण 1: सरलतम रूप में (p) और (q) सहअभाज्य होने चाहिए। चरण 2: दोनों सम सिद्ध होने पर दोनों में (2) साझा गुणनखंड होगा। चरण 3: यह असंभव है, इसलिए परिमेय मान्यता गलत है।
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