Square Root

[Asian]

Can someone explain to me why x^2=49, the value for x is plus or minus 7

[timo]

Not sure what you mean. Both, +7 and -7 solve the equation: (+7)² = 49 and (-7)² = 49.

[psynapse]

Just in case the above isn't enough, remember a negative multiplied with a negative is a positive so there is no real way to know which set of numbers you get with roots.

[alan2here]

On a semi-related topic I once belived all of mathmatics was out by +1 because

 

(n - 1) * (n + 1) = (n * n) + 1

[the tree]

On a semi-related topic I once belived all of mathmatics was out by +1 because

 

(n - 1) * (n + 1) = (n * n) + 1

When you were a child right?

Well anyways, what you've written there doesn't seem to be right since the difference of two squares: [math]a^{2}-b^{2}=(a+b)(a-b)[/math]

[psynapse]

Nvm. It should be minus 1. good spot ^^

[alan2here]

(4 - 1) * (4 + 1) = 15
           4 * 4 = 16

(3 - 1) * (3 + 1) = 8
           3 * 3 = 9

(7 - 1) * (7 + 1) = 48
           3 * 3 = 49

 

My simple proff that my rule is right,

and yes it was when I was a child I descovered it.

[Asian]

have u ever heard of difference of perfect ssquares?

[psynapse]

(n - 1) * (n + 1) = (n * n) + 1

 

 

Should read

(n - 1) * (n + 1) = (n * n) - 1

 

Like your proof shows.

[Royston]

My simple proff that my rule is right,

and yes it was when I was a child I descovered it.

 

You're not expanding, that's why you're getting the incorrect result. You are familiar with expanding and the inverse...factorising ?

[alan2here]

lol, your right psynapse, the whole of mathmatics is off by -1 I guess.

 

Whats "expanding" and "the inverse...factorising" and how does it make?

 

(4 - 1) * (4 + 1) = 16
and
            4 * 4 = 16[/Code]

[ydoaPs]

(4*4)-1=15. you forgot the -1 part.

[alan2here]

(4 - 1) * (4 + 1) = 15
     (4 * 4) - 1 = 15
           4 * 4 = 16

 

There, still proves its all of by -1

[Royston]

There, still proves its all of by -1

 

It doesn't prove maths is 'all' out by -1, because 4*4 and (4-1)(4+1) are not equivalent.

 

Expanding is just...(4-1)(4+1) so 4*4=16, 4*1=4, 1*(-1)= -1, 4*-1= -4

 

16+4-1-4=15

 

So your results are right, but your reasoning to why the results are different is wrong. My first post was in response to your first calculation, sorry I missed the second.

[ydoaPs]

(4 - 1) * (4 + 1) = 15
     (4 * 4) - 1 = 15
           4 * 4 = 16

 

There, still proves its all of by -1

 

So, you can't understand why (n²-1)!=n²? I seriously don't see the problem here.

 

(n+1)(n-1)=n²-1, not n². Watch, I'll FOIL it for you.

F(first terms multiplied together)+I(inside terms multiplied together)+O(outside terms multiplied together)+L(last terms multiplied together)

(n+1)(n-1)=n²+(1)n+(-1)n+(1)(-1)=n²-1

[alan2here]

ahh, I get it :¬)

 

+1 * -1 is never going to be = to 0

 

Thats why (n-1)*(n+1) is not = to n*n

 

Thanks :¬) now I understand.