?
$${\text{The value of }}\frac{{4 + 3\sqrt 3 }}{{7 + 4\sqrt 3 }}{\text{ is?}}$$
Answer & Solution
Correct Answer:
Option
A
$$\frac{{4 + 3\sqrt 3 }}{{7 + 4\sqrt 3 }}$$
(By rationalization of denominator)
$$\eqalign{ & = \frac{{4 + 3\sqrt 3 }}{{7 + 4\sqrt 3 }} \times \frac{{7 - 4\sqrt 3 }}{{7 - 4\sqrt 3 }} \cr & = \frac{{\left( {4 + 3\sqrt 3 } \right)\left( {7 - 4\sqrt 3 } \right)}}{{49 - 48}} \cr} $$
(By rationalization of denominator)
$$\eqalign{ & = \frac{{4 + 3\sqrt 3 }}{{7 + 4\sqrt 3 }} \times \frac{{7 - 4\sqrt 3 }}{{7 - 4\sqrt 3 }} \cr & = \frac{{\left( {4 + 3\sqrt 3 } \right)\left( {7 - 4\sqrt 3 } \right)}}{{49 - 48}} \cr} $$
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