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If (\sqrt{3}=\frac{a}{b}) with (\gcd(a,b)=1), but both (a,b) are proved divisible by (3), which contradiction is correct?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?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (\gcd(a,b)=1) and (\gcd(a,b)\ge3) cannot both hold(\gcd(a,b)=1) और (\gcd(a,b)\ge3) साथ नहीं हो सकते
If both have common factor (3), they cannot remain coprime. This makes the rational assumption false.दोनों में सामान्य गुणनखंड (3) होने से वे सहभाज्य नहीं रह सकते। यही परिमेय मान्यता को गलत करता है।
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