Question

Solve each equation. Remember to check for extraneous solutions.

Answer 1

1)

3  =  √(b - 1) -------------------------> (1)

Squaring on both sides

3^2  =  b - 1

9  =  b - 1

9 + 1  =  b

b  =  10

Substitute b = 10 in Eq (1)

3  =  √(10 - 1)

3  =  √9

3  =  3

Hence, No Extraneous Solutions

2)

√(-8 - 2a)  =  0 ------------------------------>(2)

Squaring on both sides

-8 - 2a  =  0

-2a  =  8

a  =  8/(-2)

a  =  -4

Substitute a = -4 in Eq (2)

√(-8 - 2(-4))  =  0

√(-8 + 8)  =  0

√0  =  0

0  =  0

Hence, No Extraneous Solutions

Answer :

1) The Solution is b  =  10

2) The Solution is a  =  - 4.