Final answer:
To solve the equation 3 sqrt(x²-7) = 3 sqrt(2x+1), square both sides to eliminate the square roots and simplify. Then, solve the resulting quadratic equation and check that the solutions are valid in the original equation.
Step-by-step explanation:
To solve the given equation 3 sqrt(x²-7) = 3 sqrt(2x+1), you should square both sides. This step will remove the square roots and make the equation easier to work with.
First, divide both sides by 3 to simplify the equation:
sqrt(x²-7) = sqrt(2x+1)
Next, square both sides to eliminate the square roots:
(sqrt(x²-7))² = (sqrt(2x+1))²
x² - 7 = 2x + 1
Now, rearrange the terms and solve for x:
x² - 2x - 8 = 0
After solving the quadratic equation, you should obtain two potential solutions for x. Always remember to check your solutions in the original equation to ensure they are valid, since sometimes squaring both sides of an equation can introduce extraneous solutions.