Brain teaser for the maths geeks

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LDFerguson

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Can anyone tell me why this equation is unusual? (This is not a trick question or a joke by the way.)

(a+b)^2 = a^2 + 2ab + b^2
 
I have to give up. It looks like a normal equation to me.

I even tried it using c and d and it still works :D
 
Is it the equation for the Irish economy? If so, there should be a few exponmential symbols in there as well :D
 
Is it unusual as it will be on the leaving cert maths paper but of no use to 99% of the population. Oh, wait...
 
ivuernis said:
It works for any values of a and b?
Click to expand...

Yup - I only read about this recently (in a thriller novel, oddly enough) - I believe such equations are known as identities, where you can insert any value for a or b (or other variable) and the equation will still work.

Utterly useless to me, but I found it interesting.
 
Yup - I only read about this recently (in a thriller novel, oddly enough) - I believe such equations are known as identities, where you can insert any value for a or b (or other variable) and the equation will still work.
Click to expand...
That's the answer?

I thought the whole idea of algebra was that you could insert any value for the variables. How does this make the equation any different to any other equation?

how is it different to:

(a)(a) = a^2 ?
 
Yes, this equation is perfectly common, usual, normal and familiar to any JC student.

I can't see how it's unusual?


(a+b)^2 = (a + b)(a + b) = aa + ab + ba + bb

= a^2 + 2ab + b^2
 
umop3p!sdn said:
That's the answer?

I thought the whole idea of algebra was that you could insert any value for the variables. How does this make the equation any different to any other equation?

how is it different to:

(a)(a) = a^2 ?
Click to expand...

Blazes. When I read this, I thought it was unusual for an equation with two variables to have freedom for either one to have any value. Darn you Stieg Larsson!

For example, 2(a) + (b) = 6(a) only works where (b) = 4(a), so you cannot use any numbers you like for (a) and (b).

But I think I'm actually just showing up the fact that the last time I studied algebra (badly) was approaching 25 years ago.

I think I'll stop digging. :eek:
 
LDFerguson said:
Blazes. When I read this, I thought it was unusual for an equation with two variables to have freedom for either one to have any value. Darn you Stieg Larsson!

For example, 2(a) + (b) = 6(a) only works where (b) = 4(a)

But I think I'm actually just showing up the fact that the last time I studied algebra (badly) was approaching 25 years ago.

I think I'll stop digging. :eek:
Click to expand...

Good for you for having a look at algebra and finding it interesting. It is interesting.
Your mistake was
1) To use the term "unusual"
2) To underestimate just how geeky, geeks are
 
For example, 2(a) + (b) = 6(a) only works where (b) = 4(a), so you cannot use any numbers you like for (a) and (b).
Click to expand...

I have a feeling you might be confusing how to solve equations. If you have two variables, you need two different, simultaneous equations to find the solution. Draw the two equations as graphs, and where they cross is a solution.

If you only have one equation, with two variables, then you won't be able to solve it. (a+b)^2 and a^2 + 2ab + b^2 are the both the same equation. If you plot them, it will be the same graph.
 
umop3p!sdn said:
That's the answer?

I thought the whole idea of algebra was that you could insert any value for the variables. How does this make the equation any different to any other equation?

how is it different to:

(a)(a) = a^2 ?
Click to expand...

It's different because it has two variables. Your example only has one (a).

Not all equations mean that the two expressions are equal for whatever value we give the variables involved. When it is, it is known as an identity. Otherwise it is just known as an equation.
 
Not all equations mean that the two expressions are equal for whatever value we give the variables involved. When it is, it is known as an identity. Otherwise it is just known as an equation.
Click to expand...
In the OP's example, it's the same equation at both sides of the equal sign. It's like saying:
2y = 2y
or
(x^2)w+7/t = (x^2)w+7/t
etc...
Of course the expression will be equal for whatever values are given.
 
umop3p!sdn said:
In the OP's example, it's the same equation at both sides of the equal sign. It's like saying:
2y = 2y
or
(x^2)w+7/t = (x^2)w+7/t
etc...
Of course the expression will be equal for whatever values are given.
Click to expand...

Well that's like saying an apple is an apple. There is nothing 'unusual' about the equation used by the OP. It's simply an mathematical identity i.e. it is an assertion that is independent of the values of the variables. The term 'equation' is generally only used in maths when there is specific solution i.e. the assertion is only true for specific values.

For example work out the following

(x+1)^2=x^2+2x+1

and

(x+1)^2=2x^2+x+1

One works with any value while the other only works with specific values. Which is which? (stole that example from the internet so hope it works!)
 
(x+1)(x+1)
x^2 + x + x + 1
x^2 + 2x + 1

The first equation is the 'identity', because it's the same equation.

I'm a bit disappointed with this to be honest.
 
Could someone recommend a good algebraic maths book? Is the junior cert book any good? Maybe I should start there.
 
I'd be happy to find my way to the far end of the 12 times table! (Assuming there is still such a thing - or should that be place?)
 
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