contestada

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)​

Respuesta :

gmany

Answer:

[tex]\large\boxed{A)\ u^2-11u+24=0}[/tex]

Step-by-step explanation:

[tex](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[/tex]

Answer:  The correct option is

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

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

[tex](x^2-1)^2-11(x^2-1)+24=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

Let us consider that

[tex]u=x^2-1.[/tex]

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

[tex](x^2-1)^2-11(x^2-1)+24=0\\\\\Rightarrow u^2-11u+24=0.[/tex]

Thus, the required equivalent quadratic equation is

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

Option (A) is CORRECT.

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