Question

prove that 2√3 - 1 is an irrational no ​

Answer 1

Answer:

Step-by-step explanation:

let us assume 2√3-1 is a rational number

we can find two co-primes p and q(q is not equal to 0)

so it will in the form of p/q

p/q=2√3-1

p/q+1=2√3

p/2q+1=√3

p/q r integers

p/2q+1 is rational

therefore√3 is also rational

this contradicts the fact that √3 is irrational

therefore our assumption that 2√3-1 is rational

therefore 2√3-1 is irrational

hope this helps u

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Answer 2

Answer:

hi .. The proof is given by contradiction method..

Step-by-step explanation:

PROOF:-

let ,

2√3-1 be a rational number.

2√3-1 = p/q     [ rational numbers are represented in the form p/q]

2√3  = p/q + 1

√3 = ( p + q)/2q

now here, p ,q and 2 are rational numbers

and , if a rational number is divided with another rational number then the remainder is also a rational number.

so √3 is also rational.

but this contradicts the fact that √3 is irrational number.

so,

2√3 - 1 is an irrational number....