The following equation has solutions
\(x_1= 1\) and
\(x_2 = 3\). Find
the sum of the remaining real solutions.
\[
x^{4} - 12x^{3} + 47x^{2} - 72x + 36 = 0
\]
The following equation has solution
\(x_1= 2\) and
\(x_2= 4\). Find
the sum of the remaining real solutions.
\[
x^{4} - 6x^{3} - x^{2} + 54x - 72 = 0
\]
Which part of the plane describes the solution of the following system of
inequalities?
\[\begin{aligned}
x +\phantom{ 3}y\leq &3 & &
\\y - 2x < & - 1 & &
\end{aligned}\]
Which part of the plane describes the solution of the following system of
inequalities?
\[\begin{aligned}
x + y > &2 + x & &
\\y + 1\leq &x + 1 & &
\end{aligned}\]
Which part of the plane describes the solution of the following system of
inequalities?
\[\begin{aligned}
2x - y\geq &2 & &
\\2x + y\geq & - 2 & &
\end{aligned}\]
Which part of the plane describes the solution of the following system of
inequalities?
\[\begin{aligned}
2y - x\geq &4 & &
\\2y - x\geq & - 2 & &
\end{aligned}\]
Which part of the plane describes the solution of the following system of
inequalities?
\[\begin{aligned}
x\leq &3 & &
\\5x > &9 - 3y & &
\end{aligned}\]
In the picture, the shaded region corresponds to the set of points that is the solution to one of the given systems of inequalities. Which of the systems is it?