![]() ![]() If a = 10, then a^2 - 4a = 60, not a perfect square. If a = 8, then a^2 - 4a = 32, not a perfect square. If a = 6, then a^2 - 4a = 12, not a perfect square. Not good for searching for solutions such that a,b ∈ N.Ī = (b ± √(b^2 - 4b^2))/2 = (b ± i b √3)/2 = b * (1 ± i √3)/2 which is not a natural number. This lead me to believe that b is a multiple of a. Let's start with subtracting a*b from both sides: What if we allow the possibility that a ≠ b? The only solution to a + b = a * b is a = b = 2. The only way that 1/(b - 1) ∈ N is when b = 2. This blog entry is all about trying to find solutions to equations - in an analytic manner. Note that the set of natural numbers may or may not include 0. That is all variables are natural numbers (the counting numbers). Note I am looking for integer solutions, ignoring all solutions that were not natural numbers.įor the following let a, b, and n ∈ N. Example: int(π) = 3.īelow is the instructions on how I found possible solutions on the Casio Prizm. The integer function returns the integer part of a number. Then solving for A would yield A = √(X³ - B²). I will post screen shots from a Casio Prizm to demonstrate the search for solutions.įor each case, I will present base cases (A = 0, B = 0, and A = B = 0). ![]() Type each command as you would entering commands in Program mode. On the current generation (fx-9860g II, Prizm, this includes the older models), within the RUN/MAT mode set the calculator in Linear Input mode. One great thing about Casio graphing calculators is that you can make mini-programs. The set can include or not include zero, depending in the definition used. (Where N is the set of natural numbers (counting numbers). ![]() Here's to a Happy and Safe New Years Celebration and to a kick ass 2013! To my readers, I get such pleasure from writing on this blog, and fully appreciate each and every one of you. ![]()
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