The Equations
Description of How and Why Each Radical Equation Was Built
Equation 1: I constructed this equation to satisfy multiple constraints at once. I included “A” by placing a square root on both sides of the equation. The constant (4) was added to the left radicand to meet the requirements for “C”. To satisfy “D”, I placed the two in front of the square root on the right. This equation allows like terms to combine when squared, fufilling “F”, while only using one radical expression per side, meeting “E”. “B” is met due to both radicands being binomials.
Equation 2: I formed the second equation to ensure a no solution (“H”) result. This was accomplished by placing a square root equal to a negative number, which is impossible. This also satisfies “G” (negative solution) since the equation attempts to produce a negative answer. No real number makes a square root negative, so the equation has no “real solution”.
Which constraints did you choose to complete first, and why?
I chose to focus on constraints that can be shown within a solveable equation, such as “A”, “C”, “D”, and “E” (the first equation). These were easier to include into a single solveable equation. I worked on constraints that required more difficulty later, like “B” and “H”, which needed a second equation, after I was able to show the simpler constraints. This answer is based of the first radcial equation.
What strategies did you use to tackle the more difficult tasks on the menu?
With difficult constraints like “H” and “G”, I was detail-oriented about my thought process of what qualifies for unsolvable radical equations. I realized that setting a square root equal to a negative number results in no solution, which assisted my construction of equation two. I meticulously tested multiple numbers and expressions to ensure each constraint was met without contradicting another.
Were there any constraints you struggled to pair together?
Yes, I struggled pairing “G” and “H” together, at first, they seemed to contrast each other. However, I realized that an equation seem to produce a negative solution but still have no real solution, this resulted with me completing both with one equation.
How did you approach a problem that you initially found confusing or difficult?
I approached a problem that I initially found confusing or difficult by simplifying it into lesser parts. By doing this I was able to foucs on one or two constraints at a time, instead of attempting to complete all at once. I tested easier radical equations and adjusted their terms until finding one that worked. A tip that I applied was writing out what each constraint needed, this helped me with my organization.
Can you describe a moment when you had an “aha” moment while working on a task?
My “aha” moment appeared during my realization of setting a radical equal to a negative number, because that would automatically create an equation with no solution (Equation 2). Initially, I attempted to force an equation to have no solution using complex algebra. This singular realization simplified this whole assignment.
Did you find it helpful to have the freedom to choose the order of activities? Why or why not?
Yes, having freedom to choose the order of activities was helpful, due to it allowing me to start with simpler constraints and working towards more complex ones. If I had been forced to operate in a strict order, I definitely would have came across multiple challenges. The given flexibility made this certain section of the assignment less stressful.
How did working independently on the math menu activities help you develop your skills?
Working independently allowed me to showcase my problem-creation skills. This forced me to think critically about how radicals act and test numerous setups to meet multiple constraints. This assignment strengthened my analyzing and troubleshooting skillset. This resulted in me adjusting my approach when an equation was not matching certain constraints.
Reflection on Solving the Radical Equation Constraints
I use evidence to make judgments or decisions during this assignment, when I tested and solved each radical equation to ensure it met the required constraints. For example, I realized that setting a square root equal to a negative number would automatically make the equation unsolvable, helping me efficiently satisfy “H”.