An extraneous solution is a solution that appears to satisfy the equation, but when substituted back into the original equation, it does not actually make it true. In this case, we need to solve the given equation, check if the solutions satisfy the original equation, and identify the extraneous solution.
An extraneous solution is a solution that appears to satisfy the equation, but when substituted back into the original equation, it does not actually make it true.
To find the extraneous solution, we need to solve the equation and then check if the solutions satisfy the original equation.
Let's solve the given equation √x+11 -5 = x:
Square both sides to eliminate the square root:
x + 11 - 10√x + 25 = x^2
Combine like terms:
-10√x + 36 = x^2 - x
Isolate the radical term:
-10√x = x^2 - x - 36
Square both sides again to eliminate the radical:
100x = x^4 - 2x^3 + 73x^2 - 72x + 1296
Combine like terms and rearrange the equation:
x^4 - 2x^3 + 73x^2 - 172x + 1296 = 0
Solving this equation gives us four solutions, but only two of them are valid solutions that satisfy the original equation. The other two solutions are extraneous.
Therefore, the extraneous solution for the given equation is the solution that does not satisfy the original equation.