Question

have a look at attachment for question

Answer 1

I tried to do the question by rationalizing the first one but I think that how will I be able to use the second one also. Should I rationalize second one also?

Answer 2

@TuringTest @amistre64 @experimentX

Answer 3

any1?

Answer 4

@TuringTest

Answer 5

@jim_thompson5910 @myininaya @LolWolf

Answer 6

All right, sorry for taking so long, I'm trying to find a way of solving this that's not absolutely ridiculous on the computation.

Answer 7

..take ur time

Answer 8

We do know that \(a, b, c \in \mathbb{Q}\), right?

Answer 9

is it necessary?

Answer 10

(And \(l, m, n\) also) or is it not the case?

Answer 11

I don't really know if it's necessary, but it'd make the problem a whole lot simpler.

Answer 12

no..until it's not given we can't use this

Answer 13

ok let it be... let a,b,c,l,m,n belonging to Q

Answer 14

lolwolf..? any idea?

Answer 15

Wait, no, \(l,m,n\not \in \mathbb{Q}\). Otherwise we'd have to have \(a=b=c\vee l=m=n=0\)
Bah! Yeah, I got this far:
\[
(b-c)(c-a)2l\sqrt{b}+(a-b)(c-a)2m\sqrt{c}+(b-c)(a-b)2n\sqrt{a}=0
\]

Answer 16

that's too much complicated..isn't it?

@akash123

Answer 17

math hater: @lgbasallote

Answer 18

rationalizing? any way there?

Answer 19

anyone got a problem with a math hater?

Answer 20

yes ... lgba help me :P

Answer 21

and continue?

Answer 22

It's not *that* complicated, it's just a pain to work with. It's still better than fractions, personally.

Answer 23

well I don't want to give you all pain for m problem so wait ... just tell me should I simplify it more.. (see my image)

Answer 24

The thing is that you need to make use of both given properties to derive the last one.

Answer 25

right..

Answer 26

It's not a simple simplification problem, since you have to force three equalities from two. Unless I'm missing some property, which could likely be the case.

Answer 27

I also tried to simplify it more... But that makes no sense for me... at least

Answer 28

Yeah, right now, between the lack of sleep and the homework I just finished, my brain is essentially fried. I'll see if I can come up with anything by tomorrow, interesting problem, though, will go through it, again, tomorrow in lecture.

Answer 29

@Zarkon

Answer 30

@Algebraic!

Answer 31

the two given condition looks like planes passing through the origin and the last equation (to prove) looks like a line passing through the origin. How do you prove it?

let the last equation = k (some constant) ... and put the values of l,m,n into those two planes and see what you get.

Answer 32

I didn't get you experimentx can you show example

Answer 33

you know
ax+by+cz = 0 <-- plane passing through the origin?

Answer 34

the first two equations are equation of planes passing through the origin


and this is equation of line.
try to substitute the last equation to first two one. or try something like this

ax+by+cz=0
dx+ey+fz=0

=> x/(bf-ce) = y/(cd - af) = z/(ae - bd)