Question

If $\frac{5+\sqrt{3}}{7+4\sqrt{3}}=a+b\sqrt{3}$, then -

• A. $a=23,b=-13$
• B. $a=-11,b=6$
• C. $a=11,b=-6$
• D. $a=6,b=11$

Answer 1

Answer: (A)

$a=23,b=-13$

$\left(\frac{5+\sqrt{3}}{7+4\sqrt{3}}\right)\times \left(\frac{7-4\sqrt{3}}{7-4\sqrt{3}}\right)=\left(\frac{35-20\sqrt{3}+7\sqrt{3}-12}{49-48}\right)=23-13\sqrt{3}\therefore a=23andb=-13$