Question

Please help with this easy question! I need to find x y and z. I have the 3 following equations but I don't know how to go about getting them.

2x = lambda * y * z
2y = lambda * x * z
2z = lambda * x * y

In the solutions they get x^2 = y^2 => y = +- x
=> z = +- x =>

How did they get that above? ^^

Answer 1

don't know

Answer 2

can you tel me what mean this lambda there ?
wann being lambda time y time z =2x ??? the first line

Answer 3

The original problem is actualy for me to find the point(s) on the surface xyz=1 closest to the origin. I know that the surface is the constraint. So it will g(x,y,z) and the origin will be f(x,y,z). Then I took the gradient of f and the gradient of g. Put them into the formula: gradient f = lambda gradient g. After multiplying it out, I am left with those 3 equations. It then shows x^2 = y^2 => y = +- x
=> z = +- x => and that is where im lost

Answer 4

sorry but i dont understand it clearly

Answer 5

@Preetha Can you please help me?

Answer 6

Thanks for the reply Im gonna take a look right now

Answer 7

@Loser66 i followed through what you did but I dont think that is correct. here is a screenshot of the solution to the part im having trouble with:

Answer 8

anyone?

Answer 9

@Andysebb You should post the original one. When you post part of them, how can I trace it?

Answer 10

@calculusfunctions

Answer 11

is it lagrange multiplier?

Answer 12

if it is so, you have to give out the curve f (x, y, z) and the condition g (x,y,z)

Answer 13

@loser66 here is the original if it helps

Answer 14

Here is the solution:

Answer 15

I understand everything up until the 2nd screenshot where you get x^2 , y^2 etc

Answer 16

exactly what I showed you. Mine is correct, fortunately. hehehe

Answer 17

are you with me??

Answer 18

Yes that makes a lot more sense

Answer 19

I need to take another look at your help document though

Answer 20

since y =\(\pm\)x and x =\(\pm\)y, you can distribute + to + and then, + to -. but you have triple variable , so far you have 12 candidates, but some of them overlap, therefore at the end you have 8 variable which lie on 8 quadrant of 3D

Answer 21

Thanks for your help!

Answer 22

no idea whether you are with me or just politely say thank you. anyway, I tried all my best

Answer 23

Haha no you helped me thanks. I was just confused as to how they got the x^2 and y^2, etc. Your help document explains that pretty well

Answer 24

ok