\(\sqrt{3}\) के प्रमाण में यदि (p,q) सहभाज्य हैं और दोनों (3) से विभाज्य मिलते हैं, तो (\gcd(p,q)) के बारे में विरोधाभास क्या है?
In the proof of \(\sqrt{3}\), if (p,q) are coprime but both are found divisible by (3), what is the contradiction about (\gcd(p,q))?
Explanation opens after your attempt
Correct Answer
A. (\gcd(p,q)=1) और (\gcd(p,q)\ge 3) दोनों साथ नहीं हो सकते(\gcd(p,q)=1) and (\gcd(p,q)\ge 3) cannot both hold
Concept
Being coprime means the HCF is (1). Both divisible by (3) means it is at least (3).
Why this answer is correct
The correct answer is A. (\gcd(p,q)=1) और (\gcd(p,q)\ge 3) दोनों साथ नहीं हो सकते / (\gcd(p,q)=1) and (\gcd(p,q)\ge 3) cannot both hold. Being coprime means the HCF is (1). Both divisible by (3) means it is at least (3).
Exam Tip
सहभाज्य होने से महत्तम समापवर्तक (1) है। दोनों (3) से विभाज्य होने से वह कम से कम (3) होगा।
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