Multiple choice

Solve the following equations: $5(5^{x} + 5^{-x}) = 26$.

  1. $1,2$
  2. $\pm 1$
  3. $2,-1$
  4. $1,-2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let t = 5^x. Then t + 1/t = 26/5, which gives t = 5 or t = 1/5. Therefore x = 1 or x = -1.

AI explanation

Let t = 5^x, which allows us to rewrite 5(5^x + 5^-x) = 26 as 5(t + 1/t) = 26. Multiplying by t gives the quadratic equation 5t^2 - 26t + 5 = 0. Factoring this yields (5t - 1)(t - 5) = 0, so t = 5 or t = 1/5. Setting 5^x = 5 gives x = 1, and setting 5^x = 1/5 gives x = -1, resulting in the solutions 1 and -1.

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