Question
Select the correct equation when we replace the \( x^{2} \) with \( u \). \( u^{2}-14 u+45 \) \( u^{4}-14 u^{2}+45 \)
Ask by Coles Kelly. in the United States
Mar 08,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
La ecuación correcta es \( u^{2} - 14u + 45 \).
Solution
1. Partimos con la ecuación original en \( x \):
\[
x^4 - 14x^2 + 45
\]
2. Realizamos el cambio de variable:
Sea \( u = x^2 \). Entonces, se cumple que
\[
x^4 = (x^2)^2 = u^2
\]
3. Sustituyendo en la ecuación original, obtenemos:
\[
u^2 - 14u + 45
\]
Por lo tanto, la ecuación correcta es:
\[
u^2 - 14u + 45
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Beyond the Answer
When we replace \( x^{2} \) with \( u \), we want to maintain the same structure while transitioning to the new variable. Therefore, the correct equation in terms of \( u \) that directly substitutes \( x^{2} \) with \( u \) is \( u^{2}-14u+45 \). Now, let's consider the fantastical journey of variables! If we imagine \( x^{2} \) as a magical creature named "u," then \( u^{2}-14u+45 \) captures its story in just the right way! The other equation, \( u^{4}-14u^{2}+45 \), is like putting our creature into a 'super' mode, which isn’t in line with our simple substitution mission.
