Hi guys, can you please help me with this? >> Given that, 28 + p √(3) = (q + 2 √(3) ) {}^(2) where p and q are integers, find the values of p and q. Answer should be: + or…

Question

Hi guys, can you please help me with this?

>> Given that,

`28 + p √(3) = (q + 2 √(3) ) {}^(2)`
where p and q are integers, find the values of p and q.
Answer should be: + or - 4 and + or - 16
Can I have the step by step explanation? Thanks :)​

Answer 1

see explanation

Explanation:

Expand the right side and then compare like terms with the left side.

(q + 2
`√(3)` )²

= q² + 4q
`√(3)` + 12

= q² + 12 + 4q
`√(3)`

Compare like terms with 28 + p
`√(3)`

Comparing the
`√(3)` 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 = ±
`√(16)` = ± 4

Hence

p = 4q = 4 × ± 4 = ± 16