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(\sqrt{2}) is assumed rational and written as (\sqrt{2}=\frac{p}{q}). If (p) and (q) are coprime, what is the correct next conclusion from (p^2=2q^2)?(\sqrt{2}) को परिमेय मानकर (\sqrt{2}=\frac{p}{q}) लिखा गया है। यदि (p) और (q) सहअभाज्य हैं, तो (p^2=2q^2) से सही अगला निष्कर्ष कौन सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (p^2) is even(p^2) सम है
Step 1: In (p^2=2q^2), the right side has factor (2). Step 2: So (p^2) is even and then (p) is also even. Step 3: In proofs, first write divisibility of the square, then of the number.चरण 1: (p^2=2q^2) में दाईं ओर (2) का गुणनखंड है। चरण 2: इसलिए (p^2) सम है और फिर (p) भी सम होगा। चरण 3: प्रमाण में पहले वर्ग की विभाज्यता लिखें, फिर मूल संख्या की।
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