if `(5 + 2sqrt(3))/(7 + 4sqrt(3))` =` a + bsqrt(3)` , them : Options: A . &nbspa = - 11, b = - 6 B . &nbspa = - 11, b = 6 C . &nbspa = 11, b = - 6 D . &nbspa = 6, b = 11

if `(5 + 2sqrt(3))/(7

Question

if `(5 + 2sqrt(3))/(7 + 4sqrt(3))` =` a + bsqrt(3)` , them :

Options:

A . a = - 11, b = - 6

B . a = - 11, b = 6

C . a = 11, b = - 6

D . a = 6, b = 11

Answer: Option C

`a + bsqrt(3)` = `(5 + 2sqrt(3))/(7 + 4sqrt(3))` x `(7 - 4sqrt(3))/(7 - 4sqrt(3))`

`(35 - 20sqrt(3) + 14sqrt(3) - 24)/((7)^2 - (4sqrt(3))^2)` = `(11 - 6sqrt(3))/(49 - 48)` = `11 - 6sqrt(3)`

`:.` a = 11, b = - 6

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