Question

prove that 2 - √5 is an irrational number​

Answer 1

2 - √5

_________ [ GIVEN ]

• We have to prove that 2 - √5 is an irrational number.

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Let us assume that 2 - √5 is an rational number.

→ 2 - √5 = a/b

Here, a and b are co-prime numbers.

→ √5 = (a/b) - 2

→ √5 = (a - 2b)/b

Here.. (a - 2b)/b is an rational number.

So, √5 is also a rational number.

But we know that √5 is irrational number.

So, our assumption is wrong.

2 - √5 is an irrational number.

____ [ HENCE PROVED ]

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