Answer:
n = - 1
Step-by-step explanation:
square both sides
([tex]\sqrt{4n+8}[/tex])² = (n + 3)² ← expand factors
4n + 8 = n² + 6n + 9
rearrange into standard form : an² + bn + c = 0 : a ≠ 0
subtract 4n + 8 from both sides
n² + 2n + 1 = 0
(n + 1)² = 0 ⇒ n + 1 = 0 ⇒ n = - 1
As a check, substitute n = - 1 into the equation and if both sides are equal then it is the solution.
left side = [tex]\sqrt{-4+8}[/tex] = [tex]\sqrt{4}[/tex] = 2
right side = - 1 + 3 = 2
Hence n = - 1 is the solution
