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If from (p^2=2q^2), (p=2k) and then (q=2r) are obtained, which proof does this complete?यदि (p^2=2q^2) से (p=2k) और फिर (q=2r) मिलते हैं, तो यह कौन सा प्रमाण पूरा करता है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Irrationality of (\sqrt{2})(\sqrt{2}) की अपरिमेयता
Step 1: In (p^2=2q^2), the key factor is (2). Step 2: Finding both (p) and (q) divisible by (2) identifies the proof of (\sqrt{2}). Step 3: This gives contradiction to the coprime condition.चरण 1: (p^2=2q^2) में मुख्य गुणनखंड (2) है। चरण 2: (p) और (q) दोनों (2) से विभाज्य मिलना (\sqrt{2}) के प्रमाण की पहचान है। चरण 3: इससे सहअभाज्य शर्त से विरोधाभास आता है।
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