Question

Solve for x, given the equation Square root of x plus 9 − 4 = 1.

Answer 1

Remember that an extraneous solution of an equation is a solution that emerges from the algebraic process of solving the equation but is not a valid solution of the equation.

First, we are going to solve our equation algebraically:

Step 1 simplify the equation:

$\sqrt{x} +9-4=1$

$\sqrt{x}+ 5=1$

Step 2 subtract 5 from both sides of the equation:

$\sqrt{x} +5-5=1-5$

$\sqrt{x} =-4$

Step 3 square both sides of the equation:

$\sqrt{x} ^2=(-4)^2$

$x=16$

Next, we are going to replace our solution in our original equation and check if it is a valid solution:

$\sqrt{x} +9-4=1$

$\sqrt{16} +5=1$

$4+5=1$

$9\neq 1$

Since 9 is not equal to 1, $x=16$ is not valid solution of the equation; therefor it is an extraneous solution.

We can conclude that the correct answer is: x = 16, solution is extraneous

Answer 2

The given condition may be mathematically expressed as,
                               sqrt (x) + 9 - 4 = 1
Group all the constants to the same side of the equation,
                                  sqrt (x) = -4
Squaring both sides give an answer of x = 16.
The answer for the question above is x = 16 is not an extraneous root because if we substitute this value to the x of the equation, the equation becomes true.