Question

Solve the radical equation: x - √3x-2 =4

Answer 1

To solve the radical equation x - √(3x-2) = 4, isolate the square root, square both sides to remove the radical, and then solve the resulting quadratic equation. Check all solutions in the original equation to ensure validity.

Step-by-step explanation:

To solve the radical equation x - √(3x-2) = 4, let's isolate the square root on one side first.

1. Add √(3x-2) to both sides to get x = 4 + √(3x-2).
2. Square both sides to eliminate the square root: (x = 4 + √(3x-2))² becomes x² = (4 + √(3x-2))².
3. Expand the right side: x² = 16 + 8√(3x-2) + 3x - 2.
4. Combine like terms: x² - 3x - 16 = 8√(3x-2).
5. Divide both sides by 8: ¼x² - ¼x - 2 = √(3x-2).
6. Square both sides again to get rid of the square root: (¼x² - ¼x - 2)² = (3x - 2).
7. Now you'll have a quadratic equation that you can solve using techniques such as factoring or the quadratic formula.
8. Remember to check all potential solutions in the original equation to ensure they don't produce a negative under the square root, which is not allowed in real numbers.

After following these steps, you will find the value(s) of x that satisfy the original equation.