Question

Which quadratic equation is equivalent to (x2 – 1)2 – 11(x2 – 1) + 24 = 0?
u2 – 11u + 24 = 0 where u = (x2 – 1)
(u2)2 – 11(u2) + 24 where u = (x2 – 1)
u2 + 1 – 11u + 24 = 0 where u = (x2 – 1)
(u2 – 1)2 – 11(u2 – 1) + 24 where u = (x2 – 1)

Answer 1

u^2 − 11u + 24 = 0 where u = x^2 − 1.

Reason: Let u = x^2 − 1. Then (x^2 − 1)^2 − 11(x^2 − 1) + 24 = u^2 − 11u + 24. (This factors as (u−3)(u−8)=0, giving x^2 = 4 or 9, so x = ±2, ±3.)