Question

please answer the question​

Answer 1

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Answer 2

Step-by-step explanation:

Given:

$\frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } = a + b \sqrt{3}$

To find:

the value of a and b

Solution:

$\frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } \\ = > \frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } \times \frac{7 - 4 \sqrt{3} }{7 - 4 \sqrt{3} } \\ = > \frac{(5 + 2 \sqrt{3)}(7 - 4 \sqrt{3} )}{ {(7)}^{2} - {(4 \sqrt{3)} }^{2} } \\ = > \frac{35 + 14 \sqrt{3 } - 20 \sqrt{3} - 8 \sqrt{3 \times 3} } {49 \times 48} \\ = > \frac{35 + 14 \sqrt{3} - 20 \sqrt{3} - 24 }{1} \\ = > (35 - 24) - 6 \sqrt{3} = 11 - 6 \sqrt{3} \\ = > </u><u>11 - 6 \sqrt{3} = a + b \sqrt{3} \\ = > a = 11 \: and \: b = - 6 \: ans.$