यदि \(\sqrt{2}=\frac{m}{n}\) में (\gcd(m,n)=1) है, पर प्रमाण से (m,n) दोनों सम मिलते हैं, तो विरोधाभास क्या है?
If \(\sqrt{2}=\frac{m}{n}\) with (\gcd(m,n)=1), but the proof gives both (m,n) even, what is the contradiction?
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Correct Answer
A. (\gcd(m,n)=1) और (\gcd(m,n)\ge2) साथ नहीं हो सकते(\gcd(m,n)=1) and (\gcd(m,n)\ge2) cannot both hold
Concept
Coprime means the highest common factor is (1). Both even means it is at least (2).
Why this answer is correct
The correct answer is A. (\gcd(m,n)=1) और (\gcd(m,n)\ge2) साथ नहीं हो सकते / (\gcd(m,n)=1) and (\gcd(m,n)\ge2) cannot both hold. Coprime means the highest common factor is (1). Both even means it is at least (2).
Exam Tip
सहभाज्य होने से महत्तम समापवर्तक (1) है। दोनों सम होने से वह कम से कम (2) होगा।
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