Multiple choice

The number of roots satisfying the equation $\sqrt{5 - x} = x \sqrt{5 - x}$ is:

  1. unlimited
  2. $3$
  3. $2$
  4. $1$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

sqrt(5-x) = x * sqrt(5-x). This implies sqrt(5-x) * (1 - x) = 0. Thus, 5-x = 0 (x=5) or 1-x = 0 (x=1). Both are valid roots.

AI explanation

Squaring both sides of the equation gives 5 minus x equals x squared times (5 minus x). Bringing all terms to one side yields (5 minus x) times (x squared minus 1) equals zero. The roots are x equals 5, x equals 1, and x equals negative 1, but checking for extraneous solutions in the original square root reveals that x equals negative 1 is invalid while x equals 1 and x equals 5 are valid. The equation has exactly two valid roots.

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