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Prove that 1 upon √5-√2 is …

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Prove that 1 upon √5-√2 is an irrational number.
  • 1 answers

Tarushi Jaipuria 5 years, 7 months ago

Let 1/2-√5 is a rational number. A rational number can be written in the form of p/q where p,q are integers. 1/2-√5=p/q 1/2-p/q=√5 √5=(q-2p)/2q If p,q are integers then (q-2p)/2q is a rational number. Then,√5 is also a rational number. But this contradicts the fact that √5 is an irrational number. So,our supposition is false. Therefore,1/2-√5 is an irrational number Hence proved.
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