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Nilanjan Bhowmick AIR 3, CSIR NET (Earth Science)
Shashi ranjan sinha
Okkk.... I would have mentioned that part also but it's again the similar proof. If you take alpha less than beta, then √[(a+b)²-4ab] = b-a. in that case, b-a and b+a are algebraic over Q implies half of their sum giving b is algebraic, which is given to transcendental. Again contradiction. I used a for Alpha and b for beta while texting. Hope you understand