Question

If \( a \) is a real number and \( 2\sinh^2 x - 3\cosh x + a = 0 \) has a solution, then the range of \( a \) is:

• A. \([3, \infty) \)
• B. \((0, \frac{25}{8}) \)
• C. \([3, \frac{25}{8}] \)
• D. \((-\infty, 3] \)

Hint:

For hyperbolic equations, always combine domain condition (\(\cosh x \ge 1\)) with discriminant condition.

Answer 1

The Correct Option is C