Question

Express


`(7 - 3 √(3) )/(2 + √(3) )`
in the form of

`a + b √(3)`
where a and b are integers

Answer 1

◆ NUMBER SYSTEMS ◆


`(7 - 3 √(3) )/(2 + √(3) ) \\ \\ rationalising \: the \: denominator \: , \\ \\ (7 - 3 √(3) )/(2 + √(3) ) * (2 - √(3) )/(2 - √(3) ) \\ \\ = \frac{(7 - 3 √(3))(2 - √(3)) }{ {2}^(2) - { √(3) }^(2) } \\ \\ = (14 - 7 √(3) - 6 √(3) + 9 )/(4 - 3) \\ \\ = (23 - 13 √(3) )/(1) \\ \\ = 23 - 13 √(3) = a + b √(3) \\ \\ comparing \: both \: sides \: , \\ we \: get \: , \\ \\ a = 23 \\ and \: , \: \\ b = - 13`