Answer:
Part 1)
......[1]
Equation 1 has an extraneous solution.
......[2]
Equation 2 does not have extraneous solution.
Part 2)
has an extraneous solution which is x = -1.- the equation
does not have an extraneous solution.
Part 3)
- The first equation
has an extraneous solution. The reason is that x = -1 does not satisfy the equation. - The second equation
does not have an extraneous solution. The reason is that x = 5 satisfies the equation.
Step-by-step explanation:
Part 1)
Creating Two Radical Equations
Let us consider two radical equations
......[1]
Equation 1 has an extraneous solution.
......[2]
Equation 2 does not have extraneous solution.
Part 2)
<u><em>Solving Equation [1]</em></u>
......[1]







Plugging x = 2


2 is true.
Plugging x = -1


-1 does not satisfy the solution. Therefore, -1 is an extraneous root.
Therefore,
has an extraneous solution which is x = -1.
<u><em>Solving Equation [2]</em></u>
......[2]






Plugging x = 5


As x = 5 satisfies the equation. So, the equation
does not have an extraneous solution.
Hence, x = 5 is the solution of
.
Part 3)
The first equation
has an extraneous solution. The reason is that x = -1 does not satisfy the equation.
Check this verification:
Plugging x = -1


Hence,
has an extraneous solution which is x = -1.
The second equation
does not have an extraneous. The reason is that x = 5 satisfies the equation.
Check this verification:
Plugging x = 5


Hence,
does not have an extraneous solution.
<em>Keywords: radical equation, extraneous solution</em>
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