provel 7+2√5 i irrational
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Let us assume 7-2√5 is rational.
Let 7-2√5 = a/b, where a, b are integers
and b ≠ 0 .
-2√5 = ( a/b ) - 7
=> -2√5 = ( a - 7b )/b
=> √5 = ( a - 7b )/( -2b )
=> √5 = ( 7b - a )/2b
Since , a,b are integers , (7b-a)/2a is
rational , and so √5 is rational.
This contradicts the fact that √5 is
irrational .
Hence , 7 - 2√5 is irrational.
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