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NEED ANSWER NOW PLEASEEEEEEEEEEEEE

Which statement is true about the solution of (picture below)?
A. x = –2 is an extraneous solution, and x = 6 is a true solution.
B. x = 6 is an extraneous solution, and x = –2 is a true solution.
C. Both x = –2 and x = 6 are extraneous solutions.
D. Both x = –2 and x = 6 are true solutions.

NEED ANSWER NOW PLEASEEEEEEEEEEEEE Which statement is true about the solution of (picture-example-1

2 Answers

4 votes

Answer:

(D)

Explanation:

The given equation is:


\sqrt[3]{x^2-12}=\sqrt[3]{4x}

Cubing on both the sides, we get


x^2-12=4x


x^2-4x-12=0


(x-6)(x+2)=0

therefore, the solutions are:


x=6 and
x=-2

Substitute x=6 in the given equation, we have


(6)^2-12=4(6)


36-12=24


24=24

which is true, thus x=6 is a true solution.

Put x=-2 in the given equation, we have


(-2)^2-12=4(-2)


4-12=-8


-8=-8

which is true, thus x=-2 is a true solution.

Therefore, Both x = –2 and x = 6 are true solutions.

User Ditza
by
6.4k points
2 votes


\sqrt[3]{x {}^(2) - 12 } = \sqrt[3]{4x}
Cube by both sides:

x {}^(2) - 12 = 4x

x {}^(2) - 4x - 12 = 0

(x - 6)(x + 2) = 0
The solutions are:

x = 6 \: \: and \: \: x = - 2
The answer D is correct.
User Quinn Taylor
by
6.9k points