anonymous
  • anonymous
Prove that x^4+x^2=1
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
whats x ?
anonymous
  • anonymous
variable :P
anonymous
  • anonymous
i mean is it cube root of unity ? or imaginary number i or something else ? if not, then u just said its variable, so x^4+x^2 can't equal 1.

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anonymous
  • anonymous
or do u need to solve for x ???
anonymous
  • anonymous
I don't know that is what I am trying to figure out... this was the question in my paper and I left it blank
anonymous
  • anonymous
just prove it to 1
anonymous
  • anonymous
by means of anything
anonymous
  • anonymous
good luck with that :)
anonymous
  • anonymous
what?
anonymous
  • anonymous
i think question is incomplete...we can solve for x, but can't prove that =1...
anonymous
  • anonymous
PROVE ???
anonymous
  • anonymous
x= 1 :P
anonymous
  • anonymous
nopes, x not =1 :P
anonymous
  • anonymous
then x= -1 :P
anonymous
  • anonymous
nopes, x not =-1 :P
anonymous
  • anonymous
x^4 +x^2=1 => => x^4 +x^2 -1 = 0 => (x +0.786)*(x -0.786)*(x^2 +1.618) = 0 Real solutions: Root 1: -0.786 Root 2: 0.786 Complex roots: Root 3: 0+1.272 * i Root 4: 0-1.272 * i
anonymous
  • anonymous
are u solving that for x ,saura ?
anonymous
  • anonymous
there you go ^^
anonymous
  • anonymous
u copied that ^
anonymous
  • anonymous
yeah should i give the source ? :P
anonymous
  • anonymous
it is equal to 1
anonymous
  • anonymous
take a screenshot of your question
anonymous
  • anonymous
|dw:1353238271333:dw|Looks like no solution
anonymous
  • anonymous
1 Attachment
anonymous
  • anonymous
koli, any luck with screenshot ?
anonymous
  • anonymous
Let x^2=y
anonymous
  • anonymous
y^2+y
anonymous
  • anonymous
thats a good substitution to solve for x
anonymous
  • anonymous
u get quadratic in y
anonymous
  • anonymous
x^4+x^2-1=0|dw:1353238509864:dw|
anonymous
  • anonymous
|dw:1353238651184:dw||
anonymous
  • anonymous
|dw:1353238684199:dw|
anonymous
  • anonymous
|dw:1353238793125:dw| So, only two real roots
anonymous
  • anonymous
so for any of the 4 values of x we found above, u can prove that x^4+x^2= 1
anonymous
  • anonymous
how it is equal to 1??
anonymous
  • anonymous
anonymous
  • anonymous
solving for x in x^4+x^2=1 means ginding vales of x for which x^4+x^2 equals 1 so, for the 4 values we found, x^4+x^2 will equal 1.
anonymous
  • anonymous
ginding??
anonymous
  • anonymous
*finding
anonymous
  • anonymous
:P
anonymous
  • anonymous
ok
anonymous
  • anonymous
*values
anonymous
  • anonymous
PROVED!!!!
anonymous
  • anonymous
what ?

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