Question

Solve. [tan(x/Pi-3)-x^3+4x^2+x-4]^4+(4^x-18*2^x+32)^2=0

Answer 1

since each term is raised to an even power, then each term must equal zero, so you have two simpler equations to solve:\[\tan(\frac{x}{\pi}-3)-x^3+4x^2+x-4=0\]and:\[4^x-18*2^x+32=0\]

Answer 2

i drew graph for you

Answer 3

Sorry, it's tan(x/(Pi-3))

Answer 4

tan(Pi/(x-3)) . My bad

Answer 5

so the two equation to solve are:\[\tan(\frac{\pi}{x-3})−x^3+4x^2+x−4=0\]and:\[4^x-18*2^x+32=0\]

Answer 6

I think I'll manage with the bottom one, but the first?

Answer 7

that's exactly what I was thinking! ;-)

Answer 8

And how do you solve it?

Answer 9

tan(Pi/(x-3))-x^3+4x^2+x-4

Answer 10

spread the love happy eatser y'all

Answer 11

Suddely a wild troll appears...

Answer 12

Suddenly*

Answer 13

is this for "natural" values of x again?

Answer 14

Yes, sum is needed in the end.

Answer 15

so you should be able to follow the same principals as in the last question you posted.

Answer 16

All of that must be done again?

Answer 17

\[\left(\tan(\frac{x}{\pi-3})-x^3+4x^2+x-4\right)^4+(4^x-18\times2^x+32)^2=0\]this is what you are trying to solve????

Answer 18

Yes.

Answer 19

good lord!

Answer 20

That's what I'm saying.

Answer 21

second one is easy enough, but how do you do the first?

Answer 22

And that's what I would love to find out.

Answer 23

oh i have an idea
doh

Answer 24

we are solving for x right? and of course both have to be equal to zero, since both terms are postive

Answer 25

but the second term is zero only if x = 1 or x = 4

Answer 26

and whatever answers you get MUST make both terms zero, therefore solution to second (simpler) equation will be enough.

Answer 27

x cannot be one number for the first term and another for the second right? must be the same x
either that or i am very confused

Answer 28

satellite73: snap!

Answer 29

and since only 1 and 4 work for second term, either they work for the first term or they do not, so we can check them and see which if any work

Answer 30

so just fid solutions of second (simpler) equation and see which one(s) satisfy the first equation as well.

Answer 31

I like the idea.

Answer 32

that was what i am thinking

Answer 33

1 does not seem to work

Answer 34

4 is the only working solution.

Answer 35

let me try that again correctly

Answer 36

doesn't look like 4 works either

Answer 37

satellite73: the "tan" term you have is incorrect - please se correction by ErkoT

Answer 38

oooooh whew
it is \(\tan(\frac{\pi}{x-3})\) that makes it much nicer

Answer 39

:)

Answer 40

but wait, why doesn't one work?

Answer 41

oh because it is undefined there nvm

Answer 42

so we check
\[\tan(\pi)-4^3+4\times 4^2+4-4=0\] yes? and whew it works

Answer 43

what a funky problem. a good challenge actually, i will see if i can remember it

Answer 44

where did it come from?

Answer 45

Our teacher gave us a test to solve on our own at home. I'm in the eleventh grade at the moment.