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Question

Verify by the method of contradiction P:7 is irrational.

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Solution

Let 7 be rational

It must in the form of (a/b) where a, b have no common factor

Let 7=ab(a, b have no common factor)

7=a2b2

a2=7b2

7 divide a

Therefore there exists an integer c such that a=7c

a2=49c2

49c2=7b2

b2=7c2

7 also divides b

we got that 7 divides both a and b

But we assumed that a,b have no common factor

This is a contradiction and what we assumed is incorrect

7 is irrational

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