Calculators Unexpected Result on TI-89 Titanium for Equation with Negative Exponents

[kald13]

I was working with a much longer equation and receiving a result I didn't expect, and finally narrowed it down to the following section:

2(-2^3)-3(-2^2)

2(-2^3) is correctly calculated as -16 independently, and 3(-2^2) is correctly calculated as 12 (again, independently) for a difference of -28, but my calculator is returning -4.

No matter how I enter the equation, the only way I obtain a correct result is by first defining a variable as -2 and then substituting that variable in for -2 in the equation.

Is this problem repeated on anyone else's unit? And if you've encountered this sort of problem before, is there a way to correct it?

 

[Borek]

Is -2² intended to mean -(2²) or (-2)²?

 

[lurflurf]

I will use (-) for the negative operator

I hope 3((-)2^2) is not calculated as 12 that would be very wrong

3((-)2^2)=-12 due to operator precedence

2((-)2^3)-3((-)2^2)=2((-)(2^3))-3((-)(2^2))=-4

perhaps you had intended to write

2(((-)2)^3)-3(((-)2)^2)=-28

 

[kald13]

There are a number of different ways to enter the problem to achieve the intended result. I have tried a few variations, all with the same results.

(2*((-2)^3))-(3*((-2)^2))=-4
(2*((z)^3))-(3*((z)^2))=-28

This is a piece of the derivative of a function, and -2 is one of the zeros of the derivative signifying a local maximum in the function. The intent is to solve the equation when z=-2 (among other values)

Incidentally, entering the equation in the calculator as I originally did produces the same results; the intent is not to find -(2^3) (which is -8) but (-2^3) (which is also -8, but for a different reason).

(2*-2^3)-(3*-2^2)=-4
(2*z^3)-(3*z^2)=-28

 

[lurflurf]

^Of those four only the first one is surprising. If that input gives that output I am quite confused.
What happens if you enter
2((0-2)^3)-3((0-2)^2)
?
I do not have a ti89 handy
I do know that the manual gives the example
((-1)2)^2=4
(-)2^2=-4

 

[Mark44]

I will use (-) for the negative operator

I hope 3((-)2^2) is not calculated as 12 that would be very wrong

The above is a very silly use of parentheses.

(-2)² should evaluate to +4.
-2² should evaluate to -4.

3((-)2^2)=-12 due to operator precedence

The trouble with this notation, above, is that the - sign is not binding to anything.

2((-)2^3)-3((-)2^2)=2((-)(2^3))-3((-)(2^2))=-4

perhaps you had intended to write

2(((-)2)^3)-3(((-)2)^2)=-28

 

[lurflurf]

^It is not silly, it is to distinguish between the unary and binary operators. It is the same notation used on the calculator keypad. For you special
3(-<<<the unary one>>>2^2)

to quote the manual

$$\text{Important: Use }\bbox[3px,border:2px solid black]{\phantom( - \phantom)}\text{ for subtraction and use }\bbox[3px,border:2px solid black]{(-)}\text{ for negation.}$$

 

[Borek]

Mark, not sure if you know it, but TI-89 has two different minus keys.

The one with "(-)" is an unary "change sign" operator, the other is a binary "minus". Hence the "(-)" and "-" notation is just reflecting the reality.

 

[Mark44]

Mark, not sure if you know it, but TI-89 has two different minus keys.

No, I didn't know that. That notation seems to be fairly new in calculators. Calculators have been distinguishing between the unary minus and binary subtraction operator for a long time, but using +- for the unary operation and - for subtraction.

I didn't realize that lurflurf was using (-) to mimic that key on the TI-89.

The one with "(-)" is an unary "change sign" operator, the other is a binary "minus". Hence the "(-)" and "-" notation is just reflecting the reality.

 

[pbuk]

No, I didn't know that. That notation seems to be fairly new in calculators. Calculators have been distinguishing between the unary minus and binary subtraction operator for a long time, but using +- for the unary operation and - for subtraction.

I didn't realize that lurflurf was using (-) to mimic that key on the TI-89.

The [(-)] key doesn't mimic a [+/-] key, it correctly implements the operation of negation in normal mathementical notation which is to negate the following argument, whereas the normal implementation of a [+/-] key is to negate the argument currently displayed.

Note that page 943(!) of the manual states:

To enter a negative number, press [(-)] followed by the number. Post operations and exponentiation are performed before negation. For example, the result of -x² is a negative number, and -9² = -81.

 

[Borek]

Now that I look at the picture of my TI, I think it is time to clean it