Question

Solve the equation below. Indicate which solutions, if any, are extraneous. √ x+5 = x+3

Answer 1

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Answer:

  x = -1

Step-by-step explanation:

A graphical solution can avoid extraneous solutions. The attachment shows the one solution is x = -1.

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Squaring both sides gives ...

  x +5 = (x +3)² = x² +6x +9

Putting this in standard form, we have ...

  x² +5x +4 = 0

  (x +1)(x +4) = 0 . . . . . factor

  x = -1 or -4 . . . . . . . . values of x that make the factors zero

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Since we require the root to be non-negative, we must have ...

  x +3 ≥ 0

  x ≥ -3

The only solution that satisfies this requirement is x = -1. The solution x = -4 is extraneous. The solution is x = -1.