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Nata [24]
3 years ago
6

Which of the following is an extraneous solution of the square root of -3x-2=x+2

Mathematics
1 answer:
yarga [219]3 years ago
4 0

Answer:

x=-6 is an extraneous solution

Step-by-step explanation:

we have

\sqrt{-3x-2} =x+2

squared both sides

-3x-2=(x+2)^2

-3x-2=x^2+4x+4

x^2+7x+6=0

solve the quadratic equation by graphing

The solution is x=-6 and x=-1

see the attached figure

<u><em>Verify each solution</em></u>

substitute the value of x in the original expression

For x=-6

\sqrt{-3(-6)-2} =-6+2

\sqrt{16} =-4

4=-4 ----> is not true

so

Is an extraneous solution

For x=-1

\sqrt{-3(-1)-2} =-1+2

\sqrt{1} =1

1=1 ----> is true

so

Is the solution

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<u>Solution:</u>

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