CBSE Class 10 Answered
prove that for any positive integer and √2n+1 + √2n+3 is not rational;
Asked by Sanmit Ratnaparkhi | 01 May, 2014, 08:51: PM
Expert Answer
Lets assume that the given number is rational, which can be expressed as p/q , where p and q are intergers
?2n+1 +?2n+3 = p/q
squaring the both sides, we get
2n+1 +2n+3 +2(?2n+1) (?2n+3)= p2/q2
4n+4 +2(?2n+1) (?2n+3)= p2/q2
2(?2n+1) (?2n+3) = 4n+4 - p2/q2
irrational*irrational= rational - rational
irrational = rational, which can not be true.
Therefore, the given number is irrational.
Answered by Avinash Soni | 04 May, 2014, 03:50: PM
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