The maths thread

[Pauline]

Soon, I may forget how to solve x + 2 = 5

I give up, what's the answer?

Three thinkers

[Trolldor]

The pain and agony of the pun with badness!

[GabrielJBuckley]

Happy world maths day Jim!

[BrettA]

Happy world maths day Jim!

And speaking of 'Maths Day', it's also Square Root Day today ('09/03/03) and the next one isn't 'til 2016.

[Xamonas Chegwé]

No, no, no...

The correct answer is that you multiply it by its conjugate (root 7 - root 3), and then, when you expand the brackets, = 3.

Pure magic!

err... if you're going to do it that way, don't you get 4? Just asking...

And (root 3 - root 7) would give you -4.

Next time can we have a question with just ONE right answer!



Try this one for a laugh. For what negative values of x does the function f(x) = x^x (that's x to the power x) have values that are: -
(a) Positive and real?
(b) Negative and real?
(c) Imaginary?
(d) Undefined?

There are infinite solutions but they can be expressed quite succinctly.

You can also try differentiating the function as well - not especially difficult but needs a little head-jugglery.

Answers after the Leeds meet up.

a) x=-2n
b) x=-2n+1
c) x=-n+1/2
d) everything else

Nope. There are far more solutions than that. Anybody want a clue?

[The Curious Squid]

Thanks Jim

There's something really satisfying about solving maths problems, I'm afraid I'm more rusty than I expected though since my head is close to melting after reading the 11 posts on here so far.

I'm talking forgotten how to complete the square type rusty. You feel like getting me back on track coach?

Can you give me a hand remembering how to do it?

I know this level of maths is absurdly low but I honestly can't think for the life of me how you go about solving them.

How about (8x2 + 4x + 3) my maths is actually that bad at the minute that I can't even remember if something like that can be made into a perfect square

[Xamonas Chegwé]

Thanks Jim

There's something really satisfying about solving maths problems, I'm afraid I'm more rusty than I expected though since my head is close to melting after reading the 11 posts on here so far.

I'm talking forgotten how to complete the square type rusty. You feel like getting me back on track coach?

Can you give me a hand remembering how to do it?

I know this level of maths is absurdly low but I honestly can't think for the life of me how you go about solving them.

How about (8x2 + 4x + 3) my maths is actually that bad at the minute that I can't even remember if something like that can be made into a perfect square

This doesn't have any real solutions. The quadratic formula is



It is the bit inside the square root that counts. If it is negative, there is no real solution.

In your example,

b2 - 4ac = 42 - 4 x 8 x 3 = 16 - 96 = -80

[The Curious Squid]

Can you give me an example that would work and then take me through the process?

[JimC]

Can you give me an example that would work and then take me through the process?

Here.

x2 + 6x + 3 = 0

LHS cannot be factorised using rational numbers

Starting with the x2 + 6x part, we could make it into a perfect square in the form of x2 + 6x + 9, simply by adding 9

x2 + 6x + 9 = (x + 3)2

So, I will alter my original expression to look like this:

x2 + 6x + 9 + 3 - 9 = 0 (note how that does not really alter it)

This becomes (x2 + 6x + 9) - 6 = 0

And then (x + 3)2 - 6 = 0 Now we use the difference of 2 squares, a2 - b2 = (a + b)(a - b)

(x + 3 + root6)(x + 3 - root6) = 0

This gives us 2 solutions, x = -3 - root6, or x = -3 + root6

[JimC]

Happy world maths day Jim!

Cheers!

I celebrated by making my year 9 students rationalise the denominator of complicated surd fractions! :twisted:

[Geoff]

Happy world maths day Jim!

Cheers!

I celebrated by making my year 9 students rationalise the denominator of complicated surd fractions! :twisted:

Happiness indeed!

[The Curious Squid]

Can you give me an example that would work and then take me through the process?

Here.

x2 + 6x + 3 = 0

LHS cannot be factorised using rational numbers

Starting with the x2 + 6x part, we could make it into a perfect square in the form of x2 + 6x + 9, simply by adding 9

x2 + 6x + 9 = (x + 3)2

So, I will alter my original expression to look like this:

x2 + 6x + 9 + 3 - 9 = 0 (note how that does not really alter it)

This becomes (x2 + 6x + 9) - 6 = 0

And then (x + 3)2 - 6 = 0 Now we use the difference of 2 squares, a2 - b2 = (a + b)(a - b)

(x + 3 + root6)(x + 3 - root6) = 0

This gives us 2 solutions, x = -3 - root6, or x = -3 + root6

I know this is really basic stuff but for some reason I'm having a comlpete mental block with it and I don't know why. I used to be really good at maths but my inability to comprehend this simple process is making me feel like a right nonce.

x2 + 6x + 9 = (x + 3)2

I get this bit but how do you make the leap to

x2 + 6x + 9 + 3 - 9 = 0

Where does the +3 come from? (I hope I'm not getting this because it's 4:45am and not because years of drinking have made me a simpleton.)

[Geoff]

x2 + 6x + 3 = 0

I know this is really basic stuff but for some reason I'm having a comlpete mental block with it and I don't know why. I used to be really good at maths but my inability to comprehend this simple process is making me feel like a right nonce.

x2 + 6x + 9 = (x + 3)2

I get this bit but how do you make the leap to

x2 + 6x + 9 + 3 - 9 = 0

Where does the +3 come from? (I hope I'm not getting this because it's 4:45am and not because years of drinking have made me a simpleton.)

It's in the original equation, Paco, but you have to engineer a way to get rid of it because it doesn't factorise. Adding 9 to each side does that.

[The Curious Squid]

x2 + 6x + 3 = 0

I know this is really basic stuff but for some reason I'm having a comlpete mental block with it and I don't know why. I used to be really good at maths but my inability to comprehend this simple process is making me feel like a right nonce.

x2 + 6x + 9 = (x + 3)2

I get this bit but how do you make the leap to

x2 + 6x + 9 + 3 - 9 = 0

Where does the +3 come from? (I hope I'm not getting this because it's 4:45am and not because years of drinking have made me a simpleton.)

It took me a few seconds to get what you were saying there but it just clicked. It still seems rather counter intuitive to me
It's in the original equation, Paco, but you have to engineer a way to get rid of it because it doesn't factorise. Adding 9 to each side does that.

[The Curious Squid]

It took me a few seconds to get what you were saying there but it just clicked. It still seems rather counter intuitive to me