Question

State True or False.

$\frac{5+\sqrt{3}}{7-4\sqrt{3}}=47+27\sqrt{3}$

• A. True
• B. False

Answer 1

The correct option is A True

As given $\frac{5+\sqrt{3}}{7-4\sqrt{3}}=94a+3\sqrt{3}b$
Multiply and divide L.H.S by $7+4\sqrt{3}$
$=\frac{35+7\sqrt{3}+20\sqrt{3}+12}{{\left(7\right)}^2-{\left(4\sqrt{3}\right)}^2}$
$=\frac{47+27\sqrt{3}}{49-48}$
$=47+27\sqrt{3}$
Now comparing L.H.S with R.H.S
$=47+27\sqrt{3}=94a+3\sqrt{3}b$
$a=\frac{47}{94}b=\frac{27\sqrt{3}}{3\sqrt{3}}$
$a=\frac{1}{2},b=9$