Question

Which quadratic equation is equivalent to (x^2-1)^2 -11(x^2-1)+24=0

A)u^2-11u+24=0 where u=(x^2-1)
B) (u^2)^2 -11(u^2) +24 where u = (x^2-1)
C)u^2+1-11u+24 =0 where u =(x^2-1)
D)(u^2-1)^2 -11(u^2-1) +24 where u =(x^2-1)​

Answer 1

`\large\boxed{A)\ u^2-11u+24=0}`

Explanation:

`(x^2-1)^2 -11(x^2-1)+24=0\\\\\text{Substitute}\ (x^2-1)=u\\\\\underbrace{(x^2-1)}_(u)\ ^2 -11\underbrace{(x^2-1)}_(u)+24=0\to u^2-11u+24=0`

Answer 2

Answer: The correct option is

(A)
`u^2-11u+24=0,~~\textup{where }u=(x^2-1).`

Step-by-step explanation: We are given to select the correct quadratic equation that is equivalent to the following equation :

`(x^2-1)^2-11(x^2-1)+24=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

Let us consider that

`u=x^2-1.`

Substituting the value of u in equation (i), we get

`(x^2-1)^2-11(x^2-1)+24=0\\\\\Rightarrow u^2-11u+24=0.`

Thus, the required equivalent quadratic equation is

`u^2-11u+24=0,~~\textup{where }u=(x^2-1).`

Option (A) is CORRECT.