Multiple choice

The equation $\sqrt {x + 10} - \dfrac {6}{\sqrt {x + 10}} = 5$ has

  1. An extraneous root between $-5$ and $-1$
  2. An extraneous root between $-10$ and $-6$
  3. A true root between $20$ and $25$

  4. Two true roots

  5. Two extraneous roots
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let u = sqrt(x+10). Equation: u - 6/u = 5. u^2 - 5u - 6 = 0. (u-6)(u+1) = 0. u=6 or u=-1. Since u = sqrt(x+10) must be >= 0, u=6 is the only solution. sqrt(x+10) = 6 => x+10 = 36 => x=26. The root u=-1 is extraneous. Since u = sqrt(x+10) = -1 implies x+10 = 1, x = -9. -9 is between -10 and -6.

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