## koli123able 2 years ago Prove that x^4+x^2=1

1. gohangoku58

whats x ?

2. koli123able

variable :P

3. gohangoku58

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.

4. gohangoku58

or do u need to solve for x ???

5. koli123able

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

6. koli123able

just prove it to 1

7. koli123able

by means of anything

8. gohangoku58

good luck with that :)

9. koli123able

what?

10. gohangoku58

i think question is incomplete...we can solve for x, but can't prove that =1...

11. sauravshakya

PROVE ???

12. zostale

x= 1 :P

13. gohangoku58

nopes, x not =1 :P

14. zostale

then x= -1 :P

15. gohangoku58

nopes, x not =-1 :P

16. zostale

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

17. gohangoku58

are u solving that for x ,saura ?

18. zostale

there you go ^^

19. gohangoku58

u copied that ^

20. zostale

yeah should i give the source ? :P

21. koli123able

it is equal to 1

22. gohangoku58

take a screenshot of your question

23. sauravshakya

|dw:1353238271333:dw|Looks like no solution

24. zostale

25. gohangoku58

koli, any luck with screenshot ?

26. koli123able

Let x^2=y

27. koli123able

y^2+y

28. gohangoku58

thats a good substitution to solve for x

29. gohangoku58

30. sauravshakya

x^4+x^2-1=0|dw:1353238509864:dw|

31. sauravshakya

|dw:1353238651184:dw||

32. gohangoku58

|dw:1353238684199:dw|

33. sauravshakya

|dw:1353238793125:dw| So, only two real roots

34. gohangoku58

so for any of the 4 values of x we found above, u can prove that x^4+x^2= 1

35. koli123able

how it is equal to 1??

36. koli123able

@gohangoku58

37. gohangoku58

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.

38. koli123able

ginding??

39. gohangoku58

*finding

40. gohangoku58

:P

41. koli123able

ok

42. gohangoku58

*values

43. koli123able

PROVED!!!!

44. gohangoku58

what ?