MathDB

Let (\log_2(x))^2 \minus{} 4 \cdot \log_2(x) \minus{} m^2 \minus{} 2m \minus{} 13 \equal{} 0 be an equation in

x.

Prove:
(a) For any real value of

m

the equation has two distinct solutions. (b) The product of the solutions of the equation does not depend on

m.

(c) One of the solutions of the equation is less than 1, while the other solution is greater than 1.
Find the minimum value of the larger solution and the maximum value of the smaller solution.

Problem Statement