Homework help, one of the few I have

x=11  solution is not extraneous

Step-by-step explanation:

sqrt( x-5) +7 = 11

Subtract 7 from each side

sqrt( x-5) +7-7 = 11-7

sqrt(x-5) = 4

Square each side

(sqrt(x-5))^2 = 4^2

x-5 = 16

Add 5 to each side

x-5+5 = 16+5

x = 21

Check

sqrt( 21-5) +7 = 11

sqrt(16) +7 =11

4+7 =11

11=11

Valid solution

B)  x = 21, solution is not extraneous

Step-by-step explanation:

√(x - 5) + 7 = 11

(√(x - 5) + 7) - 7 = 11 - 7

√(x - 5) = 4

(√(x - 5))² = (4)²

x - 5 = 16

(x - 5) + 5 = 16 + 5

x = 21

The solution is not extraneous.  An extraneous solution is a solution that is not included in the domain.  For this equation the domain would be [-5, ∞).  The solution found is included in the domain

b) well because you get well

the correct answer is 5 6 and 7