Question

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

Answer 1

Answer:

2√3-1 is an irrational number

Step-by-step explanation:

Let 2√3-1 is rational no.

Therefore, 2√3-1 = $\frac{a}{b}$

→2√3-1 =$\frac{a}{b}$

→2√3=$\frac{a}{b}$ +1

→2√3=$\frac{a+b}{b}$

→√3=$\frac{a+b}{b}$×$\frac{1}{2}$

→ √3= $\frac{a+b}{2b}$

√3 is irraional no. and $\frac{a+b}{2b}$ is rational.

irrationa l≠ rational

√3 ≠ $\frac{a+b}{2b}$

∴ this is a contradiction

∴2√3-1 is an irrational number

∴HENCE PROVED