Given that (p + 1/2√3)(1 – √3)\(^2\) = 3- √3,
find x the value of p.
Explanation
(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