1 00:00:00,590 --> 00:00:01,410 ‫Welcome back. 2 00:00:02,030 --> 00:00:13,400 ‫Let's now express K one as a function of Lunda one and LAMDA two and then K two as a function of Lumb 3 00:00:13,400 --> 00:00:16,040 ‫the one and LAMDA two. 4 00:00:16,680 --> 00:00:27,680 ‫So if we now take this first equation here, the one, then we can rewrite this entire equation like 5 00:00:27,680 --> 00:00:34,550 ‫this lamda one minus K, two over two. 6 00:00:34,700 --> 00:00:42,980 ‫So I just take this term and I put it on the other side of the equation sine and then that will equal 7 00:00:43,550 --> 00:00:53,840 ‫square root and then I have K two squared over four and plus K one. 8 00:00:54,710 --> 00:01:02,950 ‫And now what I can do I can square them both like this squared and squared. 9 00:01:03,680 --> 00:01:10,330 ‫And if you do that then you will get rid of this square root, you will have it like this then. 10 00:01:10,850 --> 00:01:21,020 ‫And so that means that we can express our K one like this, our K one which is here equals. 11 00:01:21,020 --> 00:01:30,110 ‫And I'm just going to put this term on the other side of the equation sine so I will have K one equals 12 00:01:30,950 --> 00:01:36,740 ‫lambda one minus K to over two. 13 00:01:37,280 --> 00:01:50,740 ‫And then this entire thing of course is squared like here and now minus K two squared over four. 14 00:01:51,710 --> 00:01:56,500 ‫So that's how I can express K one for now. 15 00:01:57,200 --> 00:02:04,640 ‫Then I go to another equation, this lambda two equation and in my lambda two equation I'm going to 16 00:02:04,790 --> 00:02:09,800 ‫replace this K one with this expression here. 17 00:02:10,400 --> 00:02:15,350 ‫And if I do the replacement then my Lambda two will look like this. 18 00:02:15,950 --> 00:02:24,040 ‫And now look, I can get rid of this term and this term because they amount to zero. 19 00:02:24,860 --> 00:02:30,230 ‫You have plus K two squared over four and minus K two squared over four. 20 00:02:31,070 --> 00:02:46,880 ‫And so you will have K two over to minus square root lambda one minus K two over two and all that is 21 00:02:46,880 --> 00:02:47,870 ‫squared. 22 00:02:48,590 --> 00:02:52,370 ‫And so you have something squared here and you have square root. 23 00:02:52,700 --> 00:03:06,440 ‫So they cancel each other out and so you will have lambda two equals K two over two minus and then lambda 24 00:03:06,440 --> 00:03:11,360 ‫one minus K two over to like this. 25 00:03:12,080 --> 00:03:20,360 ‫In other words you will have K two over to minus lambda one and then minus minus will give you plus, 26 00:03:20,360 --> 00:03:23,570 ‫so plus K two over two. 27 00:03:24,200 --> 00:03:27,440 ‫So that equals lambda two. 28 00:03:28,190 --> 00:03:38,450 ‫You can add this with this and then you can put lambda one on the other side of the equation sine so 29 00:03:38,450 --> 00:03:50,090 ‫k two over two plus K two over two will equal K two and then you will have lambda one plus lambda two 30 00:03:50,510 --> 00:03:51,290 ‫and that's it. 31 00:03:51,800 --> 00:03:57,440 ‫You have an expression for your K two and now you need an expression for K one. 32 00:03:58,220 --> 00:04:07,130 ‫And for that you go back to this expression here that you have K one equals all that and you will simply 33 00:04:07,130 --> 00:04:11,300 ‫replace K two with this expression. 34 00:04:12,050 --> 00:04:24,710 ‫So K one equals and now you will have lambda one here minus and then instead of K two you will have 35 00:04:24,710 --> 00:04:36,500 ‫lambda one plus lambda two over two and then all that squared minus and then here you have K to squared 36 00:04:36,500 --> 00:04:37,420 ‫over four. 37 00:04:37,820 --> 00:04:47,870 ‫So you're going to have lambda one plus lambda two squared and then divided by four. 38 00:04:48,860 --> 00:04:56,570 ‫And that's how you express your one as a function of LAMDA one and LAMDA two. 39 00:04:57,410 --> 00:04:58,180 ‫There you go. 40 00:04:58,490 --> 00:05:03,650 ‫You have your K one and K two in terms of number one and number two. 41 00:05:04,430 --> 00:05:13,610 ‫So you choose whatever polls you need and you put them in these equations and you get your K one and 42 00:05:13,610 --> 00:05:14,930 ‫K two values.