Chapter 1 Section 0 Example 3 on the TI-86

Note that the TI-86 and the TI-85 have slightly different keys. This page uses the keys associated with the TI-86. The differences are in the "2^nd" functions on some of the keys used here. The TI-85 keys will have the same key-face symbol unless otherwise noted.

Example 3 in the textbook gives the problem:

If x =

c - ab

a - b

find the value of the expression a(x+b)

The book example produces an answer.

In version 1 only

Version 1 of the text has the answer as A(C-B)²/(A-B), which is incorrect.

Although we can not do the symbolic manipulations on the TI-86 (or TI-85) calculator, we can use that machine to check our work. To do this we will choose some wierd values for a, b, and c. Then, we will determine the value of x from the expression (c-ab)/(a-b). Knowing the value of x we will determine the value of a(x+b). Then we can determine the value of the algebraic answer to our problem. FOr this page, we will start by looking at the solution given in Version 1 of the text, namely, a(c-b)²/(a-b). If a(x+b) simplifies to a(c-b)²/(a-b), then the two evaluations must produce the same numeric result.

Figure 1	We start by assigning some wierd values to A, B, and C. We use wierd values so that we are less likely to produce accidentally identical answers even if we had an error. Using values such as 1, 0, and 2 would not give a good test of our work. In any case, the calculator is going to do the arithmetic! We do not care if it has to work a little harder to use wierd values.
Figure 2	In Figure 2 we find the value of the expression *(C-AB)/(A-B) Remember that we need to explicitly include the multiplication of A and B. Then, we assign the value, 2.64759317698, to the variable X. The keystrokes needed to do this could be as short as . If we start a line with the "store" command then the calculator automatically supplies the Ans variable. And, we conclude Figure 2 by finding the value of A(X+B)**, namely, 29.5811931991.
Figure 3	The book goes through the steps needed to do the symbolic algebra of substituting *(C-AB)/(A-B) in for X in A(X+B) and, according to Version 1 of the book, the result is A(C-B)²/(A-B). Therefore, in Figure 3, we evaluate A(C-B)²/(A-B). If this were the correct answr, then evaluating it with our wierd values should produce the same result that we had for the original problem. THat is, it should evaluate to 29.5811931991. Unfortunately, we get -6.31406721852 instead of 29.5811931991 Something is wrong!**
Figure 4	We can go back a step in the book, and use our wierd values to evaluate the line before the final answer. Thus, we evaluate *A((C-AB+AB-B²)/(A-B))* and, in Figure 4, we see that the value is the expected 29.5811931991 Therefore, something is wrong between the step we just evaluated and the final line of the problem. An examination shows that the simplification was in error. The answer should have been A(C-B²)/(A-B) Figure 4 concludes with a test of that expression, and it does evaluate to the correct 29.5811931991.

This process of testing an algebraic simplification by evalating the original problem and the final answer with wierd values, has not only pointed out that we had an error, but also, it has helped us determine where in our work that error appeared.