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If (\sqrt{5}=\frac{x}{y}) and (x,y) are coprime, which conclusion follows immediately from (x^2=5y^2)?यदि (\sqrt{5}=\frac{x}{y}) और (x,y) सहअभाज्य हैं, तो (x^2=5y^2) से कौन-सा निष्कर्ष तुरंत निकलता है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (5\mid x)(5\mid x)
Step 1: (x^2=5y^2) shows that (x^2) has (5) as a factor. Step 2: Since (5) is prime, (x) is also divisible by (5). Step 3: Conclude about (x) first, then move to (y).चरण 1: (x^2=5y^2) बताता है कि (x^2) में (5) गुणनखंड है। चरण 2: (5) अभाज्य है, इसलिए (x) भी (5) से विभाज्य होगा। चरण 3: पहले (x) पर निष्कर्ष निकालें, फिर (y) पर जाएँ।
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