prove that 5+√3 is irrational
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Let us assume that 5 - √3 is a rational
We can find co prime a & b ( b≠ 0 )such that 5 - √3 = a/b
Therefore 5 - a/b = √3 So we get 5b -a/b = √3
Since a & b are integers, we get 5b -a/b is rational, and so √3 is rational.
But √3 is an irrational number Let us assume that 5 - √3 is a rational We can find co prime a & b ( b≠ 0) such that ∴ 5 - √3 = √3 = a/b
Therefore 5 - a/b = √3 So we get 5b -a/b = √3 Since a & b are integers, we get 5b -a/b is rational, and so √3 is rational.
But √3 is an irrational number
Which contradicts our statement
∴ 5 - √3 is irrational
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