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If a student stops at only (p^2=2q^2) while proving (\sqrt{2}) irrational, why is the proof incomplete?यदि कोई विद्यार्थी (\sqrt{2}) को अपरिमेय सिद्ध करते समय केवल (p^2=2q^2) तक लिखकर रुक जाता है, तो प्रमाण क्यों अधूरा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Because it still remains to show both (p) and (q) even and write contradictionक्योंकि अभी (p) और (q) दोनों सम दिखाकर विरोधाभास लिखना बाकी है
Step 1: (p^2=2q^2) is only a middle step. Step 2: From it, both (p) and (q) must be shown even. Step 3: The proof is not complete without writing the coprime contradiction.चरण 1: (p^2=2q^2) केवल मध्य चरण है। चरण 2: इससे (p) और (q) दोनों सम दिखाने होते हैं। चरण 3: सहअभाज्य शर्त से विरोधाभास लिखे बिना प्रमाण पूरा नहीं होता।
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