The discussion focuses on solving the inequality x² - 4x + 1 > 0 and expressing the solution in interval notation. The critical points identified are x = 3.732050808 and x = 0.2679491924. The correct approach involves determining the intervals where the inequality holds true rather than simply stating the union of the two solutions. The proper representation of the solution requires identifying intervals based on the critical points and testing values within those intervals.
PREREQUISITESStudents, educators, and anyone studying algebra who needs to solve and express inequalities in interval notation.
What you have written, the "union" of two numbers, makes no sense at all. You take the union of sets, not numbers. You need intervals not numbers. The numbers you give, which are better written [itex]2+ \sqrt{3}[/tex] and [tex]2- \sqrt{3}[/tex], are where that left side is <b>equal</b> to 0. Then separate the intervals where it is true from the intervals where it is false. Take one value in each interval to see whether it is ">" or "<".[/itex]RaDitZ said:Solve Inequalities with answers in Interval notation.
x^2 + 1 > 4x
Solve for x, U = Union
x^2 - 4x + 1 > 0
x= 3.732050808, 0.2679491924
Answer x= 3.732050808 U 0.2679491924 ?