Answer :
To rewrite the equation [tex]\(4x^4 - 21x^2 + 20 = 0\)[/tex] as a quadratic equation, we can use an appropriate substitution.
1. Notice that the equation involves terms of [tex]\(x^4\)[/tex] and [tex]\(x^2\)[/tex]. Our goal is to express it in terms of a single variable.
2. Let's consider a substitution that simplifies the equation. By substituting [tex]\(u = x^2\)[/tex], we can express [tex]\(x^4\)[/tex] as [tex]\((x^2)^2\)[/tex], which becomes [tex]\(u^2\)[/tex].
3. Substitute [tex]\(u = x^2\)[/tex] into the original equation:
[tex]\[
4(x^2)^2 - 21x^2 + 20 = 0
\][/tex]
This becomes:
[tex]\[
4u^2 - 21u + 20 = 0
\][/tex]
4. Now, the equation [tex]\(4u^2 - 21u + 20 = 0\)[/tex] is a quadratic equation in terms of [tex]\(u\)[/tex].
By using the substitution [tex]\(u = x^2\)[/tex], the original quartic equation is transformed into a quadratic equation, making it easier to solve.
1. Notice that the equation involves terms of [tex]\(x^4\)[/tex] and [tex]\(x^2\)[/tex]. Our goal is to express it in terms of a single variable.
2. Let's consider a substitution that simplifies the equation. By substituting [tex]\(u = x^2\)[/tex], we can express [tex]\(x^4\)[/tex] as [tex]\((x^2)^2\)[/tex], which becomes [tex]\(u^2\)[/tex].
3. Substitute [tex]\(u = x^2\)[/tex] into the original equation:
[tex]\[
4(x^2)^2 - 21x^2 + 20 = 0
\][/tex]
This becomes:
[tex]\[
4u^2 - 21u + 20 = 0
\][/tex]
4. Now, the equation [tex]\(4u^2 - 21u + 20 = 0\)[/tex] is a quadratic equation in terms of [tex]\(u\)[/tex].
By using the substitution [tex]\(u = x^2\)[/tex], the original quartic equation is transformed into a quadratic equation, making it easier to solve.
