Explanation:
To solve the equation √(x^2 + 4) - 3 = 1, we can follow these steps:
Step 1: Isolate the square root term.
Add 3 to both sides of the equation to move the constant term to the other side:
√(x^2 + 4) = 4
Step 2: Square both sides of the equation.
To eliminate the square root, we square both sides of the equation:
(√(x^2 + 4))^2 = 4^2
x^2 + 4 = 16
Step 3: Solve for x.
Subtract 4 from both sides of the equation:
x^2 = 16 - 4
x^2 = 12
Step 4: Take the square root of both sides.
To solve for x, we take the square root of both sides of the equation:
√x^2 = √12
x = ±√12
Therefore, the solutions to the equation √(x^2 + 4) - 3 = 1 are x = √12 and x = -√12.