Solve for A: √(A²-4) / √(A-3) = 2
Published on September 14, 2024
Question
\( \begin{array}{c}\frac{\sqrt{A^{2}-4}}{\sqrt{A-3}}=2 \\ A=?\end{array} \)
Answer
Here’s how to solve the equation step-by-step:
1. Square both sides:
To get rid of the square roots, square both sides of the equation:
This simplifies to:
2. Multiply both sides by (A-3):
3. Expand and move all terms to one side:
4. Solve the quadratic equation:
This is a quadratic equation in the form of
Where:
- a = 1
- b = -4
- c = 8
Substitute the values into the quadratic formula:
5. Simplify:
Answer:
The solutions to the equation are