How do you solve #x = 3 +sqrt(x^2 - 9)#?
Isolate the radical; square; use normal solution techniques; then check for extraneous results.
Isolate radical by subtracting 3 from both sides:
Square both sides
Factor (both sides)
Note potential solution
Divide both sides by
So the only possible solution we have found is
Checking to ensure that this is not an extraneous root introduced by squaring; replace