prove that 5-2√3 is an irrational number
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If possible let us assume that 5 - 2root3 is a rational number.
So 5 - 2root3 = a/b ( where a and b are co primes , integers and b is not equal to 0)
- 2root3 = a - 5b/b
- root3 = a - 5b / 2b
- Root3 = -(a + 5b)/2b
Root 3 = a + 5b/2b
We know that root 3 is an irrational number but we have written it in the form of p/q that is integer/integer . So our assumption is wrong and 5 - 2root 3 is irrational.
Hence proved!!
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