And N< -2 !!Adding to MarkFL's hint:
Use the quadratic formula, after putting the equation into standard form
Ax^2 + Bx + C = 0
As a check, the discriminant (B^2 - 4AC) will be N^2 - 4
(That is, the solutions are Real numbers when N is 2 or more. Otherwise, the solutions are Complex with an imaginary part.)
?
Jomo says that N must be equal or less than -2 for this to work.
Lets say that N = 3.33333 so x = 3 for this example. So I tried to put this into quadratic form and get this
x^2 - Nx = -1 and x^2 - Nx +1 = 0
so it kinda looks like the quadratic form but not quite . Any ideas?
Not so, I agreed with Otis that N > 2 but added on that N<-2 as well. So the answer is N<-2 or N>2Jomo says that N must be equal or less than -2 for this to work.
Lets say that N = 3.33333 so x = 3 for this example. So I tried to put this into quadratic form and get this
x^2 - Nx = -1 and x^2 - Nx +1 = 0
so it kinda looks like the quadratic form but not quite . Any ideas?
Gah! There are too many decimals here for a Math post. We're talking about x = 3 and N = 1/3. Math deals with exact values when it can, not decimal approximations to the numbers.Jomo says that N must be equal or less than -2 for this to work.
Lets say that N = 3.33333 so x = 3 for this example.
I'm guessing that you actually started with x=3 and found [MATH]N = 3 + \frac{1}{3} = 3 \frac{1}{3} = \frac{10}{3} \approx 3.33333[/MATH]. So when you use the quadratic formula, you'll get only approximately 3 for x, unless you use the exact fraction form (or if rounding works in your favor). But you'll also get a second solution; don't forget that!Lets say that N = 3.33333 so x = 3 for this example. So I tried to put this into quadratic form and get this
x^2 - Nx = -1 and x^2 - Nx +1 = 0
so it kinda looks like the quadratic form but not quite . Any ideas?
Dan 10/3 ~ 3.33333, not 1/3Gah! There are too many decimals here for a Math post. We're talking about x = 3 and N = 1/3. Math deals with exact values when it can, not decimal approximations to the numbers.
-Dan
No worries. I'm a Physicist and it's only off by an order of magnitude. Good enough! ?Dan 10/3 ~ 3.33333, not 1/3
For what to work, vec1?Jomo says that N must be [less than or equal to] -2 for this to work ...
That is one of the two solutions, and it comes straight from using the quadratic formula (shown below in red).... I want to find out how x = N/2 - sqrt(N^2 - 4)/2 is derived
Are you saying that you do not know how a quadratic equation is solved?I should have wrote 3 1/3 instead of 3.333333
so i will go over x^2 - Nx + 1 = 0 again and work out the details on that
I want to find out how x = N/2 - sqrt(N^2 - 4)/2 is derived
Dan, seriously can you please explain to me why being off by any power or 10 is ok for a physicist. The first time I ran across this I was asking my physics professor to find a mistake in my work. He lookrd and said it was correct. After I pointed out that the answer was wrong and was off by a decimal place he through me out his office!No worries. I'm a Physicist and it's only off by an order of magnitude. Good enough! ?
Thanks for the catch!
-Dan
Jomo, my dear boy, it was a joke! ?Dan, seriously can you please explain to me why being off by any power or 10 is ok for a physicist. The first time I ran across this I was asking my physics professor to find a mistake in my work. He lookrd and said it was correct. After I pointed out that the answer was wrong and was off by a decimal place he through me out his office!