यदि \(\sqrt{3}=\frac{a}{b}\) में (\gcd(a,b)=1) है, पर (a,b) दोनों (3) से विभाज्य सिद्ध हों, तो सही विरोधाभास कौन-सा है?
If \(\sqrt{3}=\frac{a}{b}\) with (\gcd(a,b)=1), but both (a,b) are proved divisible by (3), which contradiction is correct?
Explanation opens after your attempt
Correct Answer
B. (\gcd(a,b)=1) और (\gcd(a,b)\ge3) साथ नहीं हो सकते(\gcd(a,b)=1) and (\gcd(a,b)\ge3) cannot both hold
Concept
If both have common factor (3), they cannot remain coprime. This makes the rational assumption false.
Why this answer is correct
The correct answer is B. (\gcd(a,b)=1) और (\gcd(a,b)\ge3) साथ नहीं हो सकते / (\gcd(a,b)=1) and (\gcd(a,b)\ge3) cannot both hold. If both have common factor (3), they cannot remain coprime. This makes the rational assumption false.
Exam Tip
दोनों में सामान्य गुणनखंड (3) होने से वे सहभाज्य नहीं रह सकते। यही परिमेय मान्यता को गलत करता है।
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