-1^2: is this equal to -1 or to 1?  TOPIC_SOLVED

Simple patterns, variables, the order of operations, simplification, evaluation, linear equations and graphs, etc.

-1^2: is this equal to -1 or to 1?

Postby diaste on Sat Jan 24, 2009 2:03 pm

Ok, I did a little reading on this and thought I had the concept down but apparently I'm missing something. The big question is does equal -1 or 1?
It's -1 from the explanation I read which makes perfect sense to me, if = then = . If, this is (-1)(-1)= 1 So fine, the negative is applied to the exponent in the first example and not in the second.
The problem I'm having a little trouble with is:
with the question: Is -1 a solution?
I say it's:
Substituting -1 for y



So negative one is not a solution.


or

y = 1

Um, I think.... :)
diaste
 
Posts: 14
Joined: Sat Jan 17, 2009 1:54 pm

Sponsor

Sponsor
 

Re: -1^2  TOPIC_SOLVED

Postby DAiv on Sat Jan 24, 2009 2:40 pm

diaste wrote:The problem I'm having a little trouble with is:
with the question: Is -1 a solution?
I say it's:
Substituting -1 for y



So negative one is not a solution.


You have the right conclusion, but for the wrong reason.

To see why, add parentheses around the variable first, before you substitute in the -1:






or

y ~ 1.22

Um, I think.... :)


Yes, that's one solution. Remember, though, there are two solutions when you're taking the square root of a positive number.


DAiv
DAiv
 
Posts: 44
Joined: Tue Dec 16, 2008 7:47 pm

Re: -1^2

Postby diaste on Sat Jan 24, 2009 3:55 pm

Thanks for your reply.
I think I see it now. The substitution is -1 not . obviously the square is then and not .

There are two solutions when taking the square root of a positive number? Really? What's the other solution?

Thanks again!

Daniel
diaste
 
Posts: 14
Joined: Sat Jan 17, 2009 1:54 pm

Re: -1^2

Postby DAiv on Sat Jan 24, 2009 6:39 pm

diaste wrote:There are two solutions when taking the square root of a positive number? Really? What's the other solution?


It's probably easiest to explain with an example:



Check:




DAiv
DAiv
 
Posts: 44
Joined: Tue Dec 16, 2008 7:47 pm

Re: -1^2: is this equal to -1 or to 1?

Postby anonmeans on Sat Jan 24, 2009 7:26 pm

For -1^2, the 2 is only on the 1, not the -. If you had (-1)^2, then the 2 would be on the -.
anonmeans
 
Posts: 48
Joined: Sat Jan 24, 2009 7:18 pm

Re: -1^2: is this equal to -1 or to 1?

Postby DAiv on Sun Jan 25, 2009 11:29 am

anonmeans wrote:For -1^2, the 2 is only on the 1, not the -. If you had (-1)^2, then the 2 would be on the -.


This is true for pure mathematics. It's worth noting, however, that the Microsoft Excel spreadsheet (and some computer languages) gives the unary minus sign precedence over the exponent, so -1^2 is actually interpreted as (-1)^2. There, explicit parentheses are needed to get the desired result, i.e. -(1^2). Just something to be aware of if anyone uses that product.


DAiv
DAiv
 
Posts: 44
Joined: Tue Dec 16, 2008 7:47 pm

Re: -1^2: is this equal to -1 or to 1?

Postby little_dragon on Mon Jan 26, 2009 1:19 pm

So Excel and stuff doesn't do the order of operations? That's confusing! :nono:
User avatar
little_dragon
 
Posts: 185
Joined: Mon Dec 08, 2008 5:18 pm

Re: -1^2: is this equal to -1 or to 1?

Postby mathgirl on Tue Jan 27, 2009 5:31 pm

Anything squared is itself times itself. (-1) squared is (-1)(-1). Since a negative times a negative is a positive, (-1)(-1) is 1. :clap:
mathgirl
 
Posts: 1
Joined: Tue Jan 27, 2009 5:23 pm

Re: -1^2: is this equal to -1 or to 1?

Postby DAiv on Tue Jan 27, 2009 7:27 pm

little_dragon wrote:So Excel and stuff doesn't do the order of operations? That's confusing! :nono:


It does all the other operations in the correct order, but it swaps the order of the unary minus sign (i.e. the minus in '-5') and exponent (i.e. the 2 in x^2).

So, pure maths has the order:
parentheses,
exponent,
unary minus sign | multiplication | division,
addition | subtraction (i.e. binary minus)

and Excel has the order:
parentheses,
unary minus sign,
exponent,
multiplication | division,
addition | subtraction (i.e. binary minus).

It's important to distinguish between unary minus and binary minus, though. A unary minus operates on just one thing (operand), e.g -5, while a binary minus operates on two operands, e.g. 7 - 5.

So, in pure maths:
-5^2 = -(5^2) = -(25) = -25, because the exponent '^2' is performed before the minus sign '-'

but in Excel:
-5^2 = (-5)^2 = 25, because the minus sign '-' is peformed before the exponent '^2'

And you can also have both a binary minus and a unary minus together, as in:
6 - -2 = (6) - (-2) = 6 + 2 = 8

where the first minus is binary (as it has the two operands '6' and '-2') and the second one is unary (as it has just the one operand '2').


DAiv
DAiv
 
Posts: 44
Joined: Tue Dec 16, 2008 7:47 pm


Return to Pre-Algebra