Answer :
To transform the equation
[tex]$$
4x^4 - 21x^2 + 20 = 0
$$[/tex]
into a quadratic equation, we notice that the term [tex]$x^4$[/tex] can be written as [tex]$(x^2)^2$[/tex]. This observation suggests the substitution
[tex]$$
u = x^2.
$$[/tex]
Now, replace [tex]$x^2$[/tex] by [tex]$u$[/tex], so that:
- [tex]$x^4 = (x^2)^2 = u^2$[/tex].
Substituting these into the equation gives:
[tex]$$
4u^2 - 21u + 20 = 0.
$$[/tex]
This is a standard quadratic equation in terms of [tex]$u$[/tex]. Therefore, the correct substitution is
[tex]$$
\boxed{u = x^2}.
$$[/tex]
[tex]$$
4x^4 - 21x^2 + 20 = 0
$$[/tex]
into a quadratic equation, we notice that the term [tex]$x^4$[/tex] can be written as [tex]$(x^2)^2$[/tex]. This observation suggests the substitution
[tex]$$
u = x^2.
$$[/tex]
Now, replace [tex]$x^2$[/tex] by [tex]$u$[/tex], so that:
- [tex]$x^4 = (x^2)^2 = u^2$[/tex].
Substituting these into the equation gives:
[tex]$$
4u^2 - 21u + 20 = 0.
$$[/tex]
This is a standard quadratic equation in terms of [tex]$u$[/tex]. Therefore, the correct substitution is
[tex]$$
\boxed{u = x^2}.
$$[/tex]
