Question

To solve the equation √(4a+x) - √(a-x) = √a, you should: A. Square both sides and simplify. B. Add √(a-x) to both sides. C. Subtract √a from both sides. D. Factor out √a on the left side.

Answer 1

To solve the equation √(4a+x) - √(a-x) = √a, you should first add √(a-x) to both sides, then square both sides to eliminate the square roots and simplify the equation. Finally, solve for 'a' and verify that your solution holds true in the original equation.

Step-by-step explanation:

To solve for

a

in your equation, √(4a+x) - √(a-x) = √a, the most appropriate step to take would be

Option A: Square both sides and simplify

. Here's why: squaring both sides will eliminate the square roots, making the equation simpler and easier to handle. Here's a step-by-step guide:

1. Add √(a-x) to both sides to get √(4a+x) = √(a-x) + √a.
2. Square both sides of the equation. This will result in (4a+x) = (a - x + 2√a(√a-√x)+a).
3. Simplify the equation and solve for a.

Remember that once you have squared the equation, always check your potential solutions against the original question to confirm they are correct.

Learn more about solving square root equations