1.

The value of \(\frac{{4 + 3\sqrt 3 }}{{7 + 4\sqrt 3 }}\) is1). 5√3 – 82). 5√3 + 83). 8√3 + 54). 8√3 – 5

Answer»

Given the expression: $(\frac{{4 + 3\sqrt 3 }}{{7 + 4\sqrt 3 }})$

Multiplying the numerator and DENOMINATOR by (7 - 4√3), we get

$(\Rightarrow \frac{{4 + 3\sqrt 3 }}{{7 + 4\sqrt 3 }} = \frac{{\LEFT( {4 + 3\sqrt 3 } \right) \TIMES \left( {7 - 4\sqrt 3 } \right)}}{{\left( {7 + 4\sqrt 3 } \right) \times \left( {7 - 4\sqrt 3 } \right)}})$

We know that, (a + b) (a - b) = a2 – b2

Hence,

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

$(= \frac{{\left( {28 + 21\sqrt 3- 16\sqrt 3- 36} \right)}}{{49 - 48}})$

= 5√3 - 8


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