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Question
Find the value of a and b in the following:
`(5 + 2sqrt(3))/(7 + 4sqrt(3)) = a - 6sqrt(3)`
Solution
We have, `(5 + 2sqrt(3))/(7 + 4sqrt(3)) = a - 6sqrt(3)`
For rationalising the above equation, we multiply numerator and denominator of LHS by `7 - 4sqrt(3)`, we get
`(5 + 2sqrt(3))/(7 + 4sqrt(3)) xx (7 - 4sqrt(3))/(7 - 4sqrt(3)) = a - 6sqrt(3)`
`(5(7 - 4sqrt(3)) + 2sqrt(3)(7 - 4sqrt(3)))/(7^2 - (4sqrt(3))^2) = a - 6sqrt(3)` ...[Using identity, (a + b)(a – b) = a2 – b2]
⇒ `(35 - 20sqrt(3) + 14sqrt(3) - 24)/(49 - 48) = a - 6sqrt(3)`
⇒ `11 - 6sqrt(3) = a - 6sqrt(3) = a` = 11
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