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A student assumes that
",रीना
मानती है कि
",
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: m must be even; this makes n even too, contradicting that m/n is in lowest termsm must be even; this makes n even too, contradicting that m/n is in lowest terms
From
, m² is even, so m is even. Put m=2k: 4k²=2n², hence n²=2k² and n is also even. This contradicts m/n being in lowest terms. Exam tip: use the fact that an even square has an even root.समीकरण
से m² सम है, इसलिए m भी सम होगा। m=2k रखने पर 4k²=2n², अतः n²=2k² और n भी सम है। दोनों में 2 सामान्य गुणनखंड होना न्यूनतम रूप का विरोध है। परीक्षा टिप: सम वर्ग से सम संख्या निष्कर्षित करें।
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