proove that 5-✓3 in an irrational ?
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we have to prove that 5-√3 is irrational.
Let us assume the opposite that 5-√3 is rational.
Hence we can write 5-√3 in the form of a/b.
where a and b are co-prime numbers.
Hence ,
5-√3= a /b
-√3=a/b-5
-√3=a-5b/b
√3=-(a-5b/b)
√3=5b-a/b
↓
irrational.
where 5b-a/b is rational.
Therefore rational ≠irrational.
it is a contradiction.
our assumption is incorrect.
Hence 5-√3 is irrational.
Let us assume the opposite that 5-√3 is rational.
Hence we can write 5-√3 in the form of a/b.
where a and b are co-prime numbers.
Hence ,
5-√3= a /b
-√3=a/b-5
-√3=a-5b/b
√3=-(a-5b/b)
√3=5b-a/b
↓
irrational.
where 5b-a/b is rational.
Therefore rational ≠irrational.
it is a contradiction.
our assumption is incorrect.
Hence 5-√3 is irrational.
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