00:01
The way i've seen this problem is the first term of each of these, i'm just going to call it n.
00:06
So then the second term, well, for geometric it could be n times r, and for the second term of the other one, we end plus d.
00:16
And so what we know about those two things is nr is equal to n plus d.
00:24
But then we have one more situation.
00:27
So if we multiply by r again, i mean n times r times r, r.
00:31
And times r squared, and n plus d plus d, so n plus 2d.
00:37
And we look at the ratio of those two things, so nr squared over n plus 2d, that's in the ratio of 2 to 1, 2 to 1.
00:47
And what i can do is i can cross multiply there.
00:51
So i'm looking at nr squared needs to be equal to 2n, i'm just cross multiplying, so plus 4d.
01:00
So i think what i would do is take the other equipment where these two things are equal, and i would solve for n, for d, excuse me, by subtracting n to the left side.
01:13
So over here, i can substitute this d.
01:17
And i'll just rewrite it.
01:19
So nr squared plus it's equal to 2n plus 4, but i can replace d with nr minus n.
01:34
And i'm going to try and figure out what are the possible values are far.
01:40
So if i distribute in here, what do i have nr squared is equal to 2n plus 4nr minus 4n? well, 2n minus 4n is negative 2n.
01:59
So how long i move that over 2r squared? i had negative 2n, so i'm going to add that to the left side plus 4nr.
02:09
And i guess what's going through my mind is n could be factored out of that.
02:14
I believe me with r squared plus 4r.
02:20
Sorry, that's got to be subtracted, doesn't it? and that's a quadratic.
02:38
So i think i need to do the quadratic formula, negative b plus or minus the square root of b squared minus 4ac all over 2a...