if 5 2sqrt 3 7 4sqrt a b sqrt then, Latest Questions, General Mathematics

Question:If` (5 + 2sqrt(3))/(7 + 4sqrt(3)) = a + b sqrt(3),` then

A `a = 11, b = - 6` 
B `a = - 6, b = 11` 
C `a = - 11, b = c` 
D `a = - 11, b = - 6`

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+ AnswerA

+ Explanation`(5 + 2sqrt(3))/(7 + 4sqrt(3))`

`= (5 + 2sqrt(3))/(7 + 4sqrt(3)) xx (7 - 4sqrt(3))/(7 - 4sqrt(3))`

`= (35 - 24 + 14sqrt(3) - 20sqrt(3))/(49 - 48)`

`= 11 - 6sqrt(3)`

Thus, `a + b sqrt(3) = 11 - 6sqrt(3)`

Hence, a = 11, b = - 6.

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