Question 73641
solve the radical equation
[sq.rt.of(x-4)] + [sq.rt.of(x+4)] = 4

start by moving one of the radical to the other side of the equation
[sq.rt.of(x-4)] = 4 - [sq.rt.of(x+4)]

next square both side of the equation
[sq.rt.of(x-4)]^2 = {4 - [sq.rt.of(x+4)]}^2
(x-4) = 16 - 8[sq.rt.of(x+4)] + (x+4)

then isolate the radical on one sides of hte equatiomn
x-4 - (x+4) - 16 = -8[sq.rt.of(x+4)]
-24 = -8[sq.rt.of(x+4)]

simplify the equation  by dividinq both sides by  -8
3 = [sq.rt.of(x+4)] 

then square both sides of the equation
3^2 = [sq.rt.of(x+4)]^2
9 = x+4
x = 5

check by substituting X=5 in the given problem

[sq.rt.of(x-4)] + [sq.rt.of(x+4)] is it = 4
[sq.rt.of(5-4)] + [sq.rt.of(5+4)] is it = 4
[sq.rt.of(1)] + [sq.rt.of(9)] is it = 4
1+3 is it = 4
4=4
therefore the solution set is {5}