5

K 3 ~ 3 8 02/ 4 3 ~ 9 1 1 1 3 1 8 2 ! { 8 L...

Question

K 3 ~ 3 8 02/ 4 3 ~ 9 1 1 1 3 1 8 2 ! { 8 L

K 3 ~ 3 8 02/ 4 3 ~ 9 1 1 1 3 1 8 2 ! { 8 L



Answers

$$\frac{2}{3} k-k+\frac{3}{8}=\frac{1}{2}$$

Okay, This problem, we have equals to falling. And it's also a three by tweet matrix. So we have negative. 310 and then zero negative. 31 and four Negative. Eight two. Now we can obtain the characteristic equation again. As follows. The same exact procedure as the previous problems. We have a negative Lambda cute minus four. Lambda squared minus five. Lambda minus two equals zero. So, Landau, one comma to come on three are gonna equal native one negative one. And negative, too. Now, for Lambda equals negative too. We want to solve the following equation for the Eiken victor. A plus two i times u equals zero. Then we'll obtain u equals T where Ty's every parameter, as always, times 111 And for Lambda equals negative one. We saw this equation a plus. I times you equal zero. And when we solve this, we will get you is equal to a T times 1/2 1 and two or equivalently team times one, two and four. Because this is just the Eiken victor skilled differently, scaled up. And so we have our answers

So our equation is 10 case with 1/3 power. Um, plus eight is equal to negative three K to the 2/3 power. So here I have a quadratic form equation. My variable appears twice, and the exponents one expert is twice that of the other. So I'm going to substitute in you to make it a little easier to work with. So you I'll have people to k to the 1/3 power and you squared will be caged. The 1/3 power squared, which is K two, the 2/3 power. So greatly. Look, something to substitute for both of those. So that could just the equation. 10 you plus eight. Um, it's equal to negative. Three. You squared. Perfect. Okay, I'm going to add three. You square to both sides, so I get three. You squared. Um, plus 10 U plus eight is equal to zero. Okay, so now I'm going to factor this, um, and the way I am going to go about doing that is I need to have a factor of three. You and use. We get three, you square, and then I need to other terms. So plus a plus B. So this would go zero. Um, And so if I most with this out, I would get three You squared plus au plus three bu plus a B. So that is combining these two like terms. Three beef was a U plus A B equals zero. So here a B needs to be able to eight and three b plus A needs vehicle to 10. Okay, So ways we could get eight are one and 82 and four and that's it. So let's see how we can do this. Um, if I have two and 43 times to plus four will give me 10. So that's what we're going to be is equal to a is for so now we have factors which are three U Plus A, which is four, and you plus B, which is +20 And because thes multiply together to be zero, at least one of them has to be zero. So three U plus four a equals zero or you plus two could be zero. So that gives me three years opportunity before more. Use it to negative 4/3 or I could use this equation and I've he was connected to now you to re sub student for cakes for solving for K not you. Kate's the 1/3 power. Oops. Que two The 1/3 power Xuexian Negative 4/3 war Kate's The 1/3 power is executive to answer this offer k The last thing these do is cube both sides. And when we do that, we get simply k on this side. Great is equal to negative 43 cubed. So I have a negative times. A negative times a negative as negative and so than four cubes. Um, it's four cents for 16 times four is 64 over three Cube, which is 27. OK, could be negative. 64 27th War K could be equal to negative to Cuba to be negative. Beat It's OK is it was negative 64 27th or negative eight.

Okay, so this problem wants us. Teoh Multiply by Naval by Cor Tick So we have K plus two times 12 cake You'd minus three case Where plus K plus wine. Okay, um, to solve this, I'm just going to district distribute. Over. Addition, I'm seven. Multiply everything by K and then by two. So I have 12 k to the fore, minus three k cubed plus case, Grand plus K. Then I most want everything About two. I'm gonna have 24 k cubed, minus six k squared plus two K plus two. Okay, lets together. I'll have my final polynomial. So I have 12 k to the fore plus 21 K cubes minus five. Case where? Let's three K plus two. Okay, thank you very much.

Hello, everyone. Now we're solving up the problem which is asking us to solve for the following equation which is to over three Okay, minus gay less three over eight being equal to half. So I have two things with a K here next to each other. I need to isolate for this case. So what I want to do is to bring everything with a K on one side and everything with a constant on the other side. So those two that's over three. You with the K minus K. But putting them together will be a minus one over three K. We just added them to each other. This we still have the plus three over eight is equal to have. I want to isolate for this K to be on this side, so I need to remove that you over it from next to it. So what I will do is I will have to subtract this plea over eight from both sides. So I just do a minus. You ever ate here and this is equal to have and again I have to subtract the minus two over eight on this side because I did it on the other side. So this will be left with minus one over three Key. The three over eight will concert with the negative three over eights and on the other side, half minus three over eight. This is one over eight. So now I have this negative one over three Constant. Next to this K, I need to remove it because I need the case will be on its own. So what I'll do is negative one over three. Okay, I will multiply it by three. And on the other side. Because I multiplied one side by three. I have to multiply the other side as well with a three. So this will bring me two minus K equal to three over eight. I have the key with the minus sign here, so I need to remove this minus time from here. So what I'll do is I will multiply by minus one on both sides, so I'll have the minus K multiplied by minus one. This will be equal to the over eight multiplied by minus one. So finally, this will lead us to minus K multiplied by minus one. This is just a positive K will be equal to minus three over eight. So this is your final answer. Thank you.


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