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Prove that 3+2√5 is irrational number? |
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Answer» Jindagi bhar first chapter par atke rehna Let 3+2√5 be rational number.So,3+2√5=a/b(a and b are co-prime)A/q 3+2√5=a/b =>2√5=a/b-3 =>√5=(a-3b)/2b.a,b,3 and 2 are integers.So,(a-3b)/2b is rational.But,(a-3b)/2b=√5. (√5 is irrational).Hence, our assumption is wrong.So,3+2√5 is irrational... I hope this helps you.?? 3 + 2√5 = a/ b2√5 =a/b -3√5 =a-3b/2b√5 is rational.This contradicta the fact that √5 is irrational.So our supposition is incorrect. |
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