Let's solve the given equations step-by-step. We will simplify each equation and write them in the standard form [tex]\(au^2 + bu + c = 0\)[/tex].
1. The first equation:
[tex]\[
(u^2 + 3) + u - 2 = 0
\][/tex]
Combine like terms within the parentheses:
[tex]\[
u^2 + 3 + u - 2 = 0
\][/tex]
Simplify further:
[tex]\[
u^2 + u + 1 = 0
\][/tex]
2. The second equation is already in the standard form:
[tex]\[
u^2 + u - 2 = 0
\][/tex]
3. The third equation:
[tex]\[
(u^2 + 9) + u - 2 = 0
\][/tex]
Combine like terms within the parentheses:
[tex]\[
u^2 + 9 + u - 2 = 0
\][/tex]
Simplify further:
[tex]\[
u^2 + u + 7 = 0
\][/tex]
4. The fourth equation is already in the standard form:
[tex]\[
u^2 + u + 1 = 0
\][/tex]
Thus, after simplifying, the equations become:
1. [tex]\(u^2 + u + 1 = 0\)[/tex]
2. [tex]\(u^2 + u - 2 = 0\)[/tex]
3. [tex]\(u^2 + u + 7 = 0\)[/tex]
4. [tex]\(u^2 + u + 1 = 0\)[/tex]
So, the final forms of the equations are:
[tex]\[
u^2 + u + 1 = 0
\][/tex]
[tex]\[
u^2 + u - 2 = 0
\][/tex]
[tex]\[
u^2 + u + 7 = 0
\][/tex]
[tex]\[
u^2 + u + 1 = 0
\][/tex]
