Question

If '$a$' and '$b$' are two rational number and $\frac{2+\sqrt{3}}{2-\sqrt{3}}=a+b\sqrt{3}$, then $b=$____.

• A. $4$
• B. $7$
• C. $6$
• D. $8$

Answer 1

The correct option is A $4$

We have $\frac{2+\sqrt{3}}{2-\sqrt{3}}$, On multiplying and dividing it with $2+\sqrt{3}$, We get

$\Rightarrow \frac{(2+\sqrt{3}{)}^2}{2^2-3}=\frac{4+3+4\sqrt{3}}{1}=7+4\sqrt{3}$

$\Rightarrow a=7$ and $b=4$