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Answer :
We start with the equation
[tex]$$
4x^4 - 21x^2 + 20 = 0.
$$[/tex]
Notice that the highest power is [tex]$x^4$[/tex], but it can be expressed as [tex]$(x^2)^2$[/tex]. This observation suggests making the substitution
[tex]$$
u = x^2.
$$[/tex]
Then, we have
[tex]$$
x^4 = (x^2)^2 = u^2.
$$[/tex]
Substituting into the original equation yields
[tex]$$
4u^2 - 21u + 20 = 0.
$$[/tex]
This is a quadratic equation in [tex]$u$[/tex]. Thus, the correct substitution is
[tex]$$
u = x^2.
$$[/tex]
[tex]$$
4x^4 - 21x^2 + 20 = 0.
$$[/tex]
Notice that the highest power is [tex]$x^4$[/tex], but it can be expressed as [tex]$(x^2)^2$[/tex]. This observation suggests making the substitution
[tex]$$
u = x^2.
$$[/tex]
Then, we have
[tex]$$
x^4 = (x^2)^2 = u^2.
$$[/tex]
Substituting into the original equation yields
[tex]$$
4u^2 - 21u + 20 = 0.
$$[/tex]
This is a quadratic equation in [tex]$u$[/tex]. Thus, the correct substitution is
[tex]$$
u = x^2.
$$[/tex]
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