Question

hey,I need some help

solve the equation \[f(x)=f(\frac{ 1 }{ x })\],when\[f(x)=\frac{ x+1 }{ x ^{2} }\]

So what I do: \[f(\frac{ 1 }{ x) }=(\frac{ 1 }{ x }+1):\frac{ 1 }{ x ^{2} }=(\frac{ 1+x }{ x }):\frac{ 1 }{ x ^{2} }=x+x^{2}\]

then\[\frac{ x+1 }{ x ^{2} }=x+x ^{2}\]

and then I got a bit confused, because i dont know how to solve\[x+1+x ^{3}+x ^{4}=0\]

Any help?

Answer 1

@amistre64 could you please have a look?

Answer 2

@ParthKohli hey little reddit lover, could you have a look?

Answer 3

hey @Lyrae

Answer 4

dont leave me:(

Answer 5

oo,someone!

Answer 6

Okay, so there are some complicated ways of solving equations like these, using advenced formulas and stuff. But when you get them at this level there are usually som simple soulution and the simplest way to find one is do some "qualified gusing". If you think of some small integears, are there one which might be a soultion?

Answer 7

\[f(\frac1x)=\frac{ \frac1x+1 }{ \frac1{x^2} }\]
\[=\frac{x^2}{x^2}\frac{ \frac1x+1 }{ \frac1{x^2} }\]
\[=\frac{ \frac{x^2}x+1 }{ 1 }\]
\[=x+1~:~x\ne0\]

Answer 8

other than that, im not sure what it is your asking about

Answer 9

well, since the answer is 0, 1 must be eliminated, so 0 can't be true (also because multiplying by 0 is not 'allowed')

Answer 10

so my guess is 1 or -1

Answer 11

(because 1 must be eliminated)

Answer 12

f(x) = f(1/x) solve for x

Answer 13

yes

Answer 14

\[x+1=\frac{\frac1x+1}{x^2}\]
\[x^2(x+1)=\frac1x+1\]
\[x~x^2(x+1)=1+x\]

Answer 15

well, when x^3 = 1 seems likely

Answer 16

If you then find a solution you divide the polynomial by that soultion to get one with a lower order. Repeat this until you can solve using quadratic formula.

Answer 17

I dont understand:/

Answer 18

who dont you understand?

Answer 19

both of you - I didnt understand Lyrae's first message, but not the second one

and I dont understand where x^3 dissapears in your equation

Answer 20

hard to type up all that coding again .... can you retype the process i did and show me were it goes off for you?

Answer 21

alright

Answer 22

I will draw,oke?

Answer 23

k