Final answer:
To solve the equation x - 5 = √(4x - 15) and find the extraneous solution, square both sides of the equation, rearrange, simplify, and factor the resulting quadratic equation. Substitute each potential solution back into the original equation to determine the extraneous solution.
Step-by-step explanation:
To solve the equation x - 5 = √(4x - 15) and find the extraneous solution, we can start by squaring both sides of the equation to eliminate the square root symbol. This gives us (x - 5)^2 = 4x - 15. Expanding the left side of the equation gives x^2 - 10x + 25 = 4x - 15. Rearranging the equation and simplifying, we get x^2 - 14x + 40 = 0. Now we can factor the quadratic equation as (x - 10)(x - 4) = 0. Setting each factor equal to zero gives us x = 10 and x = 4 as the potential solutions.
However, when we substitute x = 10 back into the original equation, we get an undefined value on the right side, which means x = 10 is an extraneous solution. Therefore, the only valid solution is x = 4.