Question

ans me that que with explanation ​

Answer 1

$\therefore \: the \: values \: are : - \boxed{ \small{ \blue{a = 53}}} \: and \: \boxed{ \small{ \green{b = 6}}}$

Step-by-step explanation:

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

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

$\frac{5(7 - 4 \sqrt{3}) + 2 \sqrt{3}(7 - 4 \sqrt{3} ) }{ {(7)}^{2} - {(4 \sqrt{3} )}^{2} } = a + b \sqrt{3}$

$\frac{35 - 20 \sqrt{3} + 14 \sqrt{3} + 18 }{49 - 48} = a + b \sqrt{3}$

$\frac{35 + 18 - 6 \sqrt{3} }{1} = a + b \sqrt{3}$

${53 - 6 \sqrt{3} } = a + b \sqrt{3}$

$a = 53 \: and \: b = 6$

Answer 2

Step-by-step explanation:

(7+4

3

)

(5+2

3

)

=a+b

3

\frac{(5 + 2 \sqrt{3})(7 - 4 \sqrt{3}) }{(7 + 4 \sqrt{3} )(7 - 4 \sqrt{3}) } = a + b \sqrt{3}

(7+4

3

)(7−4

3

)

(5+2

3

)(7−4

3

)

=a+b

3

\frac{5(7 - 4 \sqrt{3}) + 2 \sqrt{3}(7 - 4 \sqrt{3} ) }{ {(7)}^{2} - {(4 \sqrt{3} )}^{2} } = a + b \sqrt{3}

(7)

2

−(4

3

)

2

5(7−4

3

)+2

3

(7−4

3

)

=a+b

3

\frac{35 - 20 \sqrt{3} + 14 \sqrt{3} + 18 }{49 - 48} = a + b \sqrt{3}

49−48

35−20

3

+14

3

+18

=a+b

3

\frac{35 + 18 - 6 \sqrt{3} }{1} = a + b \sqrt{3}

1

35+18−6

3

=a+b

3

{53 - 6 \sqrt{3} } = a + b \sqrt{3}53−6

3

=a+b

3

a = 53 \: and \: b = 6a=53andb=6