Question

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

Answer 1

I am not sure but you can write it

Answer 2

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

(a) u² – 11u + 24 = 0 where u = (x² – 1)

(b) (u²)² – 11(u²) + 24 where u = (x² – 1)

(c) u² + 1 – 11u + 24 = 0 where u = (x² – 1)

(d) (u² – 1)² – 11(u² – 1) + 24 where u = (x² – 1)

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(x² – 1)² – 11(x² – 1) + 24 = 0

Define u:

Let u = (x²  - 1 )

Substitute u for all the (x²  - 1 ) in the equation:

(u)² – 11(u) + 24 = 0

Simplify:

u² - 11u + 24 = 0

Answer: (a) u² – 11u + 24 = 0 where u = (x² – 1)

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Additional work:

Solve for u:

u² – 11u + 24 = 0

(u - 3) (u - 8) = 0

u = 3 or u = 8

Answer: u = 3 or u = 8

Solve for x:

u = x² - 1

If u = 3,

⇒ 3 = x² - 1

⇒ x² = 4

⇒ x = ±2

If u = 8

8 = x² - 1

x² = 9

x = √9

x = ±3

Answer: x = ±2 or ±3