Question

Solve the following equation, xe[2,0pi]. tan^3x-9tan^2x+17tanx-6=0

Answer 1

Well I tried putting x=1, I got an error.

Answer 2

\[x \approx3.14159 n+1.10715\]
\[x \approx3.14159 n+0.429998\]
\[x \approx3.14159 n+1.4191\]

Answer 3

first see if you can solve this
\[u^3-9u^2+17u-6=0\]

Answer 4

Thanks myin; that's the way.

Answer 5

if you try u=2, you will see you have one solution

Answer 6

thats what i wasn gonna say replace tan with a variable

Answer 7

then using synthetic division you can find the other 2 solutions

Answer 8

I dunno what that is.

Answer 9

synethic division+quadratic formula (or perhaps factoring if we have other rational zeros)

Answer 10

u can also urs long division to get factors

Answer 11

Wait a sec guys, I'm trying to understand this all...

Answer 12

A fancy way of saying that as u = 2 is a solution, (u-2) must be a factor of the polynomial. Hence you can write
\[ u^3−9u^2+17^u−6 = (u-2)q(u) \]
for some second order polynomial

Answer 13

make that 17u, not 17^u

Answer 14

lol

Answer 15

What happened to tan?

Answer 16

i'll let the other chefs take over

Answer 17

we will get back to the tan business after we solve that polynomial=0 for u

Answer 18

Ok, so I'm doing the whole F(#) thing at this point right?

Answer 19

what?

Answer 20

what does F(#) mean?

Answer 21

Looking for the value of x that makes everything 0.

Answer 22

u = 2

u = 1/2 (7-sqrt(37))

u = 1/2 (7+sqrt(37))

Answer 23

If you think how myininaya magically found that \( u=2 \) there is a analytical way of doing it which is known as Rational root test.

Answer 24

right fool

Answer 25

What if I got an error on my calculator?

Answer 26

Useless its tanx (as an entirety) that I using....

Answer 27

Your trying to plug number right into the equation?

Answer 28

i went through the possible rational zeros and found a rational zero
i didn't go through all possible rational zeros as i only needed one so i can just mess with a quadratic

Answer 29

Lagrange, yes...

Answer 30

Not the right idea huh?

Answer 31

You need to NotThink a bit.

Answer 32

...ok? I do that a lot.

Answer 33

Follow those steps that myin showed, youll end with the right answers

Answer 34

I'm just looking at this and my notes, and I have not a clue.

Answer 35

Is u=tanx?

Answer 36

yes

Answer 37

Ok.

Answer 38

it's more like Let u = tan x then form a polynomial in u, factor it and then substitute back the u =tan x and then solve it ..

Answer 39

ERkk.

Answer 40

Imma do this slowly...
If yo ugotta do something while you help me, do it now as I work this thru...

Answer 41

IS factor Thereom involved?

Answer 42

yes...if u-2 is a factor of P(u) ...P(2)=0

Answer 43

Let tan (x) = u \[u ^{3}-9u ^{2}+17u-6=0\] \[\left( u-2 \right)\left( u^2 - 7u -3\right) =0\]

Answer 44

wait wait waitt....
And that's also not how I was taught (or shown in the notes).
I'll try it out after I'm done my thing tho/.

Answer 45

Sorry about that. My internet went wonky.

Answer 46

And now I divide the thing by u-2 right?

Answer 47

u^2-7u+3
____________________
u-2| u^3-9u^2+17u-6
-(u^3-2u^2)
-------------------
-7u^2+17u-6
-(-7u^2+14u)
---------------
3u-6
-(3u-6)
--------
0

Answer 48

ok

Answer 49

pax did i make a mistake?

Answer 50

our factorizations are a lttle different
i have
\[\left( u-2 \right)\left( u^2 - 7u +3\right) =0\]

Answer 51

myininaya, I wish If I can give you more medals for your patience.

Answer 52

Lol.

Answer 53

are you talking about me and my division above? lol

Answer 54

I think just waiting for me to finish up my stuff here. Thanks by the way.

Answer 55

oh i had a thing i was doing lol

Answer 56

sorry u r right. it's +3

Answer 57

ITs +3?

Answer 58

just making sure
when it gets late i tend to screw up on little things

Answer 59

like sometimes i don't know how to add or multiply sometimes

Answer 60

we were talking about this:
\[\left( u-2 \right)\left( u^2 - 7u +3\right) =0 \]

Answer 61

ok. that scared me for a sec.

Answer 62

yep myininaya I was talking about that :D

Answer 63

lol

Answer 64

so we know we have u=2
we also have
\[u=\frac{7 \pm \sqrt{49-4(3)}}{2}\]
don't forget to replace u with tan(x)
and solve for x

Answer 65

Finally, I'm done the division.

Answer 66

lol

Answer 67

good

Answer 68

you have
\[u-2=0 \text{ or } u^2-7u+3=0\]

Answer 69

we need to use the quadratic formula to solve the second equation

Answer 70

I hope I remember this for the test.

Answer 71

so this is trig class?

Answer 72

i could be wrong but this is too long to put on a test

Answer 73

there might be a similar problem he/she puts there

Answer 74

but shorter

Answer 75

Whoops. I didn't type that...Double post or something.

Answer 76

i could be wrong

Answer 77

sometimes teachers get problems from special books

Answer 78

I'm sleepy guys
I'm sure if you need more help NotTim (who we decided was not myininaya earlier ;)lol) , fool and pax will continue to help unless they are are going.

Answer 79

K. Thanks man.

Answer 80

Do I look like a man to you?

Answer 81

Please say no

Answer 82

lol

Answer 83

Are you?

Answer 84

I actually have bad vision and human identification problems.

Answer 85

When I'm walking around I will misidentify everyone as the same person.

Answer 86

Ok. Its cool. No worries.

Answer 87

any1 know what I should do at (m-2)(m^2-7m+3)?

Answer 88

For m^2-7m+3, do I have to do the quadratic formula?

Answer 89

I guess I already know what to do with m-2, so I'm fine there.

Answer 90

ERm, are you people just gunna lurk there? It's fine, just....

Answer 91

find all places that u can be 0, then, recalling that u = tanx, solve for x.

Answer 92

you already found one solution is u=2, you can find the others by using the quadratic formula on the quadratic part of your factoring.

Answer 93

Ok.

Answer 94

Hey, if one of my answers is 6.54, and I wanna get the other angle with it, what do i Do?

Answer 95

Hi?

Answer 96

Um, sorry if I sound abrupt, but could anyone please answer my most recent question?