Multiple choice

The equation $\displaystyle \frac {x}{a}+\frac {a}{x}=\frac {a}{b}+\frac {b}{a}$ has two roots. They are

  1. $b, \dfrac {a^2}{b}$
  2. $a, b$
  3. $a, \dfrac {b^2}{a}$
  4. $\dfrac {a}{b}, \dfrac {b}{a}$
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A Correct answer
Explanation

The equation is x/a + a/x = a/b + b/a. By inspection, if x = b, then b/a + a/b = a/b + b/a, which is true. If x = a^2/b, then (a^2/b)/a + a/(a^2/b) = a/b + b/a, which is also true. Thus, the roots are b and a^2/b.

AI explanation

Using the zero-factor property, we set up two separate equations for the given expression: x - b = 0 and ax - b^2 = 0. Solving the first equation gives x = b. Solving the second equation by dividing by a yields the second root as a^2 divided by b. The roots are b and a^2/b.

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