SOLUTION: solve the radical equation [sq.rt.of(x-4)] + [sq.rt.of(x+4)] = 4 [sq.rt.of(x-4)] = 4 - [sq.rt.of(x+4)] [sq.rt.of(x-4)]^2 = {4 - [sq.rt.of(x+4)]}^2 (x-4) = 16

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Question 73641This question is from textbook introduction and intermediate algebra
: solve the radical equation
[sq.rt.of(x-4)] + [sq.rt.of(x+4)] = 4
[sq.rt.of(x-4)] = 4 - [sq.rt.of(x+4)]
[sq.rt.of(x-4)]^2 = {4 - [sq.rt.of(x+4)]}^2
(x-4) = 16 - 8[sq.rt.of(x+4)] + (x+4)
x-4 - (x+4) - 16 = -8[sq.rt.of(x+4)]
-24 = -8[sq.rt.of(x+4)]
3 = [sq.rt.of(x+4)]
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; then the solution set is {5} This question is from textbook introduction and intermediate algebra

Answer by srhjnqcbng11(1) (Show Source):
You can put this solution on YOUR website!
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}

SOLUTION: solve the radical equation [sq.rt.of(x-4)] + [sq.rt.of(x+4)] = 4 [sq.rt.of(x-4)] = 4 - [sq.rt.of(x+4)] [sq.rt.of(x-4)]^2 = {4 - [sq.rt.of(x+4)]}^2 (x-4) = 16 - 8[sq.rt.of(x+4)]