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In the proof for (\sqrt{2}), when both (p) and (q) are proved even, which statement about (\frac{p}{q}) is correct?(\sqrt{2}) के प्रमाण में (p) और (q) दोनों सम सिद्ध होने पर (\frac{p}{q}) के बारे में कौन-सा कथन सही है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: It cannot be in lowest formयह सरलतम रूप में नहीं हो सकता
Step 1: Both being even means both have (2) as a common factor. Step 2: A fraction in lowest form cannot have such a common factor. Step 3: This breaks the rational assumption.चरण 1: दोनों सम होने का अर्थ है कि दोनों में (2) साझा गुणनखंड है। चरण 2: सरलतम भिन्न में ऐसा साझा गुणनखंड नहीं हो सकता। चरण 3: इसी से परिमेय मान्यता टूटती है।
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