Question

$5 + 2 \sqrt{3 \:} divide \: 7 + 4 \sqrt{3} = a + b \sqrt{3}$
find the value of a and b if

Answer 1

Solution:-

given by:-
$\frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } = a + b \sqrt{3} \\ \frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{ 3} } \times \frac{7 - 4 \sqrt{3} }{7 - 4 \sqrt{3} } = a + b\sqrt{3} \\ \frac{35 + 14 \sqrt{3} - 20 \sqrt{3} - 8 \times 3 }{49 - 16 \times 3} = a + b \sqrt{3} \\ 35 - 3 \sqrt{3} - 24 = a + b \sqrt{3} \\ 11 -3 \sqrt{3} = a + b \sqrt{3} \\ here \: a = 11 \\ b = - 3$
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Answer 2

Step-by-step explanation:

Solution:-

given by:-

$\begin{gathered} \frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } = a + b \sqrt{3} \\ \frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{ 3} } \times \frac{7 - 4 \sqrt{3} }{7 - 4 \sqrt{3} } = a + b\sqrt{3} \\ \frac{35 + 14 \sqrt{3} - 20 \sqrt{3} - 8 \times 3 }{49 - 16 \times 3} = a + b \sqrt{3} \\ 35 - 3 \sqrt{3} - 24 = a + b \sqrt{3} \\ 11 -3 \sqrt{3} = a + b \sqrt{3} \\ here \: a = 11 \\ b = - 3\end{gathered}$

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