This might be the wrong place for this post (a bit technical/mathematical) but here goes anyway. The polynomials (power series)

-1 + x - x^2 and

-x^2 + x - 1 (here ^ denotes "raising to the power of")

are mathematically equivalent. They have just been presented with the terms in a different order. In English, the first expression would read "negative one add x subtract x-squared" and the second reads "negative x-squared add x subtract 1".

There is NO NEEED to use brackets here to make these two expressions equal. They already are.

Now, in Excel, follow these steps:

1) Put the value 2 into cell A1 (Press RETURN)

2) Type the following into cell B1:

=-1+A1-A1^2 (RETURN)

3) Type the following into cell B2:

=-A1^2+A1-1 (RETURN)

You will find the value in cell B1 is -3 and that of B2 is 5. Shouldn't these two answers be equal? Which one (if any) is correct? Any views?

[Please don't introduce brackets to force answers to be the same or for any other purpose ... I'm trying to prove a point here and the two expressions ARE the same mathematically WITHOUT BRACKETS.]

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# Polynomials In Excel

Started by
cyman1964uk
, Dec 03 2005 08:57 PM

2 replies to this topic

### #1

Posted 03 December 2005 - 08:57 PM

Simon

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### #2

Posted 04 December 2005 - 04:24 AM

Actually I don't think your two expressions

Whatever you prove I don't think your going to change Microsofts mind on this.

**are**the same mathematically. Well okay maybe the mathematical expressions are but the Excel expressions are not - there is an ambiguity in starting an expression with -x^2 and it requires some reading of the fine print to determine whether this is interpreted as -(x^2) or (-x)^2.Whatever you prove I don't think your going to change Microsofts mind on this.

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### #3

Posted 08 January 2006 - 12:55 PM

Cool post! It was a nice brain teaser for a Sunday morning.

Actually, these expressions are not the same.

Please recall the order of operator preference (parentheses, exponent, multiplication, division, addition, subtraction).

The experssions would be solved this way:

Expression 1

if x = 2

-1 + x - x^2

No parentheses to consider

Solve for the exponent: 2^2 = 4

No multiplication to consider

No division to consider

Solve for the addition: -1 + 2 = 1

Solve for the subtraction: 1 - 4 = -3

Solution = -3

Expression 2

if x = 2

-x^2 + x - 1

No parentheses to consider

Solve for the exponent: -2^2 = 4

No multiplication to consider

No division to consider

Solve for the addition: 4 + 2 = 6

Solve for the subtraction: 6 - 1 = 5

Solution = 5

Thanks again!

Dan

Actually, these expressions are not the same.

Please recall the order of operator preference (parentheses, exponent, multiplication, division, addition, subtraction).

The experssions would be solved this way:

Expression 1

if x = 2

-1 + x - x^2

No parentheses to consider

Solve for the exponent: 2^2 = 4

No multiplication to consider

No division to consider

Solve for the addition: -1 + 2 = 1

Solve for the subtraction: 1 - 4 = -3

Solution = -3

Expression 2

if x = 2

-x^2 + x - 1

No parentheses to consider

Solve for the exponent: -2^2 = 4

No multiplication to consider

No division to consider

Solve for the addition: 4 + 2 = 6

Solve for the subtraction: 6 - 1 = 5

Solution = 5

Thanks again!

Dan

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