Answer:
Option A. the solution a = -4 is an extraneous solution.
Step-by-step explanation:
Lets solve the radical equation to get the potential solutions.
√(a + 5) = (a + 3)
By squaring terms on both the sides
[√(a + 5)]² = (a +3)²
(a + 5) = (a + 3)²
(a + 5) = a² + 6a + 9
0 = a² + 6a + 9 - a - 5
a² + 5a + 4 = 0
a² + 4a + a + 4 + 0
a(a + 4) + 1(a + 4) = 0
(a + 1)(a + 4) = 0
a = -1 or a = -4
Now if we put the value of a = - 4 in the radical equation then we get
√(-4 + 5) = (-4 + 3)
√1 = -1
1 = -1 ( Therefore a = -4 is not the solution)
Now by putting a = -1
√(-1 +5) = -1 + 3
√4 = 2
2 = 2 which shows the equal relation.
Therefore a = -4 is an extraneous solution.
Option A. is the correct option.
