SELECT * FROM question_mgmt as q WHERE id=5175 AND status=1 SELECT id,question_no,question,chapter FROM question_mgmt as q WHERE courseId=9 AND subId=6 AND chapterId=268 and ex_no='3' AND status=1 ORDER BY CAST(question_no AS UNSIGNED)
Prove that 3 + 2√5 is irrational.
Let us assume 3 + 2√5 is a rational number.
Therefore, 3 + 2√5 = p/q where p and q are co primes and q ≠ 0.
3 + 2√5 = ab
On solving, 2√5 =(a/b) - 3
√5 =1/2 (a/b - 3)
Since a, b are integers and 1/2 (a/b-3 ) is also a rational number.
But we know √5 is an irrational number.
Thus our assumption is wrong. 3 + 2√5 is not a rational number.
Hence proved.
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