यदि \(\sqrt{5}=\frac{x}{y}\) और (x,y) सहअभाज्य हैं, तो \(x^2=5y^2\) से कौन-सा निष्कर्ष तुरंत निकलता है?
If \(\sqrt{5}=\frac{x}{y}\) and (x,y) are coprime, which conclusion follows immediately from \(x^2=5y^2\)?
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Correct Answer
A. \(5\mid x\)
Concept
\(x^2=5y^2\) shows that \(x^2\) has (5) as a factor.
Why this answer is correct
Since (5) is prime, (x) is also divisible by (5).
Exam Tip
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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