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Nastasia [14]
3 years ago
10

The potential solutions to the radical equation are a = −4 and a = −1. Which statement is true about these solutions? The soluti

on a = −4 is an extraneous solution. The solution a = −1 is an extraneous solution. Both a = −4 and a = −1 are true solutions. Neither a = −4 nor a = −1 are true solutions.
Mathematics
1 answer:
inessss [21]3 years ago
8 0

Answer:

Both a = −4 and a = −1 are true solutions

Step-by-step explanation:

Given

\sqrt{a + 5} = a + 3

a = -4; a = -1

Required

The true statement about the solutions

We have:

\sqrt{a + 5} = a + 3

Square both sides

a + 5 = (a + 3)^2

a + 5 =a^2 + 6a + 9

Collect like terms

a^2 + 6a - a + 9 - 5 = 0

a^2 + 5a + 4 = 0

Expand

a^2 + 4a + a + 4 = 0

Factorize

a(a + 4) + 1(a + 4) = 0

Factor out a + 4

(a + 1)(a + 4) = 0

Split:

a + 1 = 0; a + 4 = 0

Solve:

a =-1; a = -4

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