2021 WAEC Further Mathematics Theory Given that (p + 1/2√3)(1 - √3)\(^2\) = 3- √3,  find x the value of...

Given that (p + 1/2√3)(1 - √3)\(^2\) = 3- √3,

find x the value of p.

(p + 1/2√3)(1 - √3)\(^2\) = 3- √3

(1- √3)\(^2\) = 4 -2√3

(p + 1/2√3) (4 -2√3) = 3 - √3

4p - 2p√3 - 2√3 - 3 = 3 - √3

4p - 2p√3 = 3 - √3 + 3 + 2√3

= 2p(2 - √3) = 6 + √3

2p= \(\frac{6+ √3}{2-√3}\)

p = \(\frac{2(6+ √3)}{2-√3}\)

= \(\frac{12+ 2√3}{2-√3}\)

= \(\frac{(12+ 2√3)(2+√3)}{(2-√3)(2+√3)}\)

: 30 + 16√3

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