Answer:
see explanation
Step-by-step explanation:
Expand the right side and then compare like terms with the left side.
(q + 2[tex]\sqrt{3}[/tex] )²
= q² + 4q[tex]\sqrt{3}[/tex] + 12
= q² + 12 + 4q[tex]\sqrt{3}[/tex]
Compare like terms with 28 + p[tex]\sqrt{3}[/tex]
Comparing the [tex]\sqrt{3}[/tex] terms gives
p = 4q
and comparing the constant terms gives
q² + 12 = 28 ( subtract 12 from both sides )
q² = 16 ( take the square root of both sides )
q = ± [tex]\sqrt{16}[/tex] = ± 4
Hence
p = 4q = 4 × ± 4 = ± 16
