Question

prove that 2√3-1 is an irrational number​

Answer 1

Step-by-step explanation:

let the2✓3-1 be rational

so it can be written as in the form of p/q where pans q are co prime means having only one common factor 1

then2✓3-1/1=0

2✓3=1

✓3=1/2

it means,✓3 is a rational no but it contradict the universal fact that ✓3 is a irrational no

so it is a contradiction due to our wrong supposition

so2✓3-1 is a irrational no

please mark me if you understood

Answer 2

THIS ANSWER IS BASED ON CLASS 10 NCERT

Hi ,

Let us assume , to the contrary , that

2√3 - 1 is a rational ,

That is , we can find coprime 

integers a and b ( b ≠ 0 ) such that

2√3 - 1 = a / b

2√3 = a / b + 1 

2√3 = ( a + b ) / b

√3 = ( a + b ) / 2b

Since a and b are integers , we get 

( a + b ) / 2b is rational , and so √3 is

rational .

But this contradicts the fact that √3 

is irrational.

This contradiction has arisen 

because of our incorrect assumption

that 2√3 - 1 is rational.

So , we conclude that 2√3 -1 is 

irrational.

I hope this helps you.

:)

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