Question

Solve the radical equation.

X+4=√x+10
What is the extraneous solution to the radical equation?
O The solution -1 is an extraneous solution.
O Both -1 and -6 are true solutions.
O The solution -6 is an extraneous solution.
O Neither -1 nor -6 is a true solution to the equation.
The answer is c

Answer 1

Explanation:

that kind of wording is always misleading.

please give my regards and comments to your teacher.

a square root has ALWAYS 2 solutions : a positive AND a negative one.

in that sense the negative solution to a square root is NOT an extraneous solution.

only any value of x < -10 (to make the argument of the square root negative) as solution would be extraneous.

so, if your teacher wants to say that only the positive solutions of a square root are allowed, it has to be said as an extra definition or by applying the "+" sign to the square root.

so,

x + 4 = sqrt(x + 10)

since the 2 solutions are already given to us, we only need to use them in the equation and see what happens.

x = -1

-1 + 4 = sqrt(-1 + 10)

3 = sqrt(9) = 3 (actually, it is ±3)

so, x = -1 is a real solution.

x = -6

-6 + 4 = sqrt(-6 + 10)

-2 = sqrt(4) = 2 (actually, it is ±2)

so, based on your teacher's expectation of only positive results of the square root (even though it was not stated),

x = -6 is an extraneous solution.

therefore, the third answer (c) is the "correct" answer.

but actually, formally, the second answer (b) is the truly correct answer.