Q. 74.3( 52 Votes )

Prove that

Answer :

Assume that 23 - 1 is rational
23 = a/b , where a and b are integers .
23 = a/b + 1
2√3 = a/b + b/b
3 = (a + b) / 2b
we know that a, b, and 2 are integers and they are also rational {i.e RHS is rational}
therefore3 will be rational.
but we know that3 is irrational.
there is a contradiction
so, 23 - 1 is an irrational number.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

<span lang="EN-USRS Aggarwal - Mathematics