Question

Prove that 6-5√7 is an irrational number

Answer 1

Answer:

Let us assume (6-5√7) is a

rational.

6-5√7 = a/b where a,b are

integers and b≠0.

=> 5√7 = 6-a/b

=> √7 = (6b-a)/5b

Since, a,b are integers ,

(6b-a)/5b

is rational , and so √7 is rational.

But this contradicts the that

√7 is irrational.

This contradiction has arisen

because of our incorrect

assumption that 6-5√7 is

rational.

So,we conclude that 6-5√7

is irrational.

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