Question

which quadratic equation is equivalent to ((x^2 - 1)^2 - 11(x^2 - 1) + 24 = 0)?
\\(\circ\\) (u^2 - 11u + 24 = 0) where (u = (x^2 - 1))
\\(\circ\\) ((u^2)^2 - 11(u^2) + 24) where (u = (x^2 - 1))
\\(\circ\\) (u^2 + 1 - 11u + 24 = 0) where (u = (x^2 - 1))
\\(\circ\\) ((u^2 - 1)^2 - 11(u^2 - 1) + 24) where (u = (x^2 - 1))

Explanation:

Step1: Identify Substitution

Let \( u = x^2 - 1 \). Substitute \( u \) into the original equation \((x^2 - 1)^2 - 11(x^2 - 1) + 24 = 0\).

Step2: Replace Terms

Replace \( x^2 - 1 \) with \( u \) in each term. The first term \((x^2 - 1)^2\) becomes \( u^2 \), the second term \(-11(x^2 - 1)\) becomes \(-11u\), and the constant term remains \( 24 \). So the equation becomes \( u^2 - 11u + 24 = 0 \) with \( u = x^2 - 1 \).

Answer:

A. \( u^2 - 11u + 24 = 0 \) where \( u = (x^2 - 1) \)