Question

5+2√3
------------- = a-b √3
7+4√3
then find the values of a and b​

Answer 1

Answer:

a =11

b=6

.............

Answer 2

Answer:

a = 11, b = 6

Step-by-step explanation:

$\frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } \\ = \frac{(5 + 2 \sqrt{3} )(7 - 4 \sqrt{3} )}{(7 + 4 \sqrt{3})(7 - 4 \sqrt{3}) } \\ = \frac{35 - 20 \sqrt{3} + 14 \sqrt{3} - 24}{ {7}^{2} - {(4 \sqrt{3} )}^{2} } \\ = \frac{11 - 6 \sqrt{3} }{49 - 48} \\ = \frac{11 - 6 \sqrt{3} }{1} \\ = 11 - 6 \sqrt{3}$

$= > 11 - 6 \sqrt{3} = a - b \sqrt{3} \\ = > a = 11 \: and \: b = 6$

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