Answer :
We start with the equation
[tex]$$
4x^4 - 21x^2 + 20 = 0.
$$[/tex]
Notice that the highest power of [tex]$x$[/tex] is [tex]$4$[/tex], and the term [tex]$x^4$[/tex] can be seen as [tex]$(x^2)^2$[/tex]. So, we make the substitution
[tex]$$
u = x^2.
$$[/tex]
With this substitution, we have
[tex]$$
x^4 = (x^2)^2 = u^2.
$$[/tex]
Substitute [tex]$u$[/tex] into the original equation:
[tex]$$
4u^2 - 21u + 20 = 0.
$$[/tex]
Now, the equation is a quadratic in [tex]$u$[/tex]. Therefore, the substitution that rewrites the original equation as a quadratic is
[tex]$$
u = x^2.
$$[/tex]
This is the correct substitution.
[tex]$$
4x^4 - 21x^2 + 20 = 0.
$$[/tex]
Notice that the highest power of [tex]$x$[/tex] is [tex]$4$[/tex], and the term [tex]$x^4$[/tex] can be seen as [tex]$(x^2)^2$[/tex]. So, we make the substitution
[tex]$$
u = x^2.
$$[/tex]
With this substitution, we have
[tex]$$
x^4 = (x^2)^2 = u^2.
$$[/tex]
Substitute [tex]$u$[/tex] into the original equation:
[tex]$$
4u^2 - 21u + 20 = 0.
$$[/tex]
Now, the equation is a quadratic in [tex]$u$[/tex]. Therefore, the substitution that rewrites the original equation as a quadratic is
[tex]$$
u = x^2.
$$[/tex]
This is the correct substitution.
