Question

Solve the radical equation. m - 3 = √ 19 - 3m. Which is an extraneous solution to the radical equation?

Answer 1

The answer is m=5 and m=-2. There is no extraneous solution for this equation.

Answer 2

Answer:

  The extraneous solution is m = -2

Step-by-step explanation:

This is normally solved by squaring both sides and solving the resulting quadratic.

$(3-m)^2=19-3m\\\\m^2-3m-10=0 \quad\text{subtract 19-3m}\\\\(m-5)(m+2)=0 \quad\text{factor}$

The values of m that make the factors zero are 5 and -2. For m=5, the equation becomes ...

  5-3 = √(19-3·5)   ⇒   2 = √4 . . . . . true

For m = -2, the equation becomes ...

  -2-3 = √(19-3(-2))   ⇒   -5 = √25 . . . . . not true

The extraneous solution is m = -2.

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Solving the equation graphically, it becomes readily apparent that the only solution is m=5. Extra work is required to see the extraneous solution is m=-2.