Final answer:
The equivalent quadratic equation to the given expression (x^2-1)^2-11(x^2-1)+24=0 is u^2-11u+24=0, where u=x^2-1, which corresponds to option a.
Step-by-step explanation:
The quadratic equation given is (x^2-1)^2-11(x^2-1)+24=0. To find an equivalent quadratic equation, we can use a substitution method where we let u be equal to x^2 - 1. This simplifies the original equation to one in terms of u:
u^2 - 11u + 24 = 0.
Comparing this with the given options, we conclude that option a is the equivalent quadratic equation because if we substitute u with x^2 - 1, we get back the original equation. So the correct quadratic equation is u^2 - 11u + 24 = 0, where u = x^2 - 1.