If sqrt(2x²) - sqrt(3x) + k = 0 has 2 solutions, which are sin(phi) and cos(phi) (0

Question

If sqrt(2x²) - sqrt(3x) +  k = 0 has 2 solutions, which are sin(phi) and cos(phi) (0<phi<pi/2), what is the value of k?

chillout · Answer

yes, @Loser66

chillout · Answer

Well, I don't know where to start this to be honest, Lol.

chillout · Answer

It is a problem from monbukagakusho, a scholarship program. It's supposed to be algebra.

chillout · Answer

I'll try. But I don't have the answers because I took the examination today.

chillout · Answer

Yes, it was.

chillout · Answer

I do not want to know it for fun, I wanna learn how to solve it :P

rsadhvika · Answer

sqrt(2x²) - sqrt(3x) +  k = 0 

sqrt(2x²)  +  k = -sqrt(3x)

square both sides and get a quadratic in  x

loser66 · Answer

oh, sin (phi) and cos (phi) are roots, there fore. sin(phi)*cos (phi) = c/a

rsadhvika · Answer

once you have the quadratic,
since you're given roots = $\sin \phi , \cos \phi$ , use sum of roots and product of roots, you will get another quadratic in k, you can solve k.

loser66 · Answer

yep. we meet there. hehe

chillout · Answer

Oh well, I didn't think of that... :P

loser66 · Answer

@rsadhvika how can you write the long sentence and have latex at the middle? all the time It jumps to next line when I use latex.

rsadhvika · Answer

there are multiple ways to do this, that quadratic method is the most elegant i can think of

another way wud be :-
since you're given  two roots, plug them directly in the given radical equation - play with identities and cancel out $\phi$ terms, you will end up with some equation in k

rsadhvika · Answer

use this @Loser66 

```
$ latex code here $
```

rsadhvika · Answer

:) latex is fun isn't it :P

chillout · Answer

I tried plugging in directly, but it gets really tiring and the examination is pretty long, to the point we have little time. Thanks you both, going to try it here. Medal goes to who? :o

loser66 · Answer

I don't want medal

loser66 · Answer

give it to rsadhvika

rsadhvika · Answer

lol if i were that girl and want to hide, i wouldnt tell the truth anyways :)

chillout · Answer

Thanks, guys. I have another question but it is in calculus part.

loser66 · Answer

ask him , post it, he will answer you

chillout · Answer

http://openstudy.com/study#/updates/51e607aee4b08833fb23cec3 Here it is.

rsadhvika · Answer

i had a look at that - cursory glance, i gelt that question is more of geometry o.o

rsadhvika · Answer

*felt

chillout · Answer

I'm asked to find its critical point, though.

rsadhvika · Answer

yeah calculus scares meh lets see