prove that 2-3√5 is an irrational number
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Answered by
4
Answer:
Let us assume that 2 - 3√5 is a rational number.
So it can be written in the form a/b
2 - 3√5 = a/b
Here a and b are co prime numbers and b ≠ 0
Solving 2 - 3√5 = a/b we get,
⇒-3√5= a-2b/b
⇒√5=a-2b/-3b= 2b-a/3b
This shows (2b-a/3b) is a rational number. But we know that But √5 is an irrational number.
So it contradicts our assumption.
Our assumption of 3 + 2√5 is a rational number is incorrect.
3 + 2√5 is an irrational number
Hence proved
✌
Answered by
80
Let,
be a rational number.
Since x is rational , 2 - x is rational and hence
is also rational number
is a Rational Number , which is a contradiction.
must be an irrational number.
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