Is this correct?

Question

Solve: (√b-20)+ 4 = √b

(A) ∅

(B) b = (52)/(5)

(C) b = -16

(D) b = (81)/(4)

(E) None of the above

For this I got; (D) b = (81)/(4). Is this correct?

Answer 1

yes, you have the correct answer

√(b-20)+4=√b

√(b-20)=√b-4

square both sides

b-20=b-8√b+16

subtract "b" from both sides

-20=-8√b+16

-20-16=-8√b

-36=-8√b

square both sides

1296=64b

b=1296/64

b=20.25 (this is the same as 81/4)

check: √(20.25-20)+4=√20.25

√0.25 + 4=√20.25

0.5+4=4.5

4.5=4.5

Answer 2

If the 20 is outside of the square root as you have typed it,

Subtract √b from both sides, we now have:

-20 + 4 = 0

This is never true, therefore choice (A) makes the most sense to me (there is no value of b that makes that equation true)