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NotTim

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

  • 2 years ago
  • 2 years ago

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

    • 2 years ago
  2. ricnus
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    \[x \approx3.14159 n+1.10715\] \[x \approx3.14159 n+0.429998\] \[x \approx3.14159 n+1.4191\]

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

    • 2 years ago
  4. JamesJ
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    Thanks myin; that's the way.

    • 2 years ago
  5. myininaya
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    if you try u=2, you will see you have one solution

    • 2 years ago
  6. LagrangeSon678
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    thats what i wasn gonna say replace tan with a variable

    • 2 years ago
  7. myininaya
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    then using synthetic division you can find the other 2 solutions

    • 2 years ago
  8. NotTim
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    I dunno what that is.

    • 2 years ago
  9. myininaya
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    synethic division+quadratic formula (or perhaps factoring if we have other rational zeros)

    • 2 years ago
  10. nubeer
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    u can also urs long division to get factors

    • 2 years ago
  11. NotTim
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    Wait a sec guys, I'm trying to understand this all...

    • 2 years ago
  12. JamesJ
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    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

    • 2 years ago
  13. JamesJ
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    make that 17u, not 17^u

    • 2 years ago
  14. myininaya
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    lol

    • 2 years ago
  15. NotTim
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    What happened to tan?

    • 2 years ago
  16. JamesJ
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    i'll let the other chefs take over

    • 2 years ago
  17. myininaya
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    we will get back to the tan business after we solve that polynomial=0 for u

    • 2 years ago
  18. NotTim
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    Ok, so I'm doing the whole F(#) thing at this point right?

    • 2 years ago
  19. myininaya
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    what?

    • 2 years ago
  20. myininaya
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    what does F(#) mean?

    • 2 years ago
  21. NotTim
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    Looking for the value of x that makes everything 0.

    • 2 years ago
  22. ricnus
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    u = 2 u = 1/2 (7-sqrt(37)) u = 1/2 (7+sqrt(37))

    • 2 years ago
  23. FoolForMath
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    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.

    • 2 years ago
  24. myininaya
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    right fool

    • 2 years ago
  25. NotTim
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    What if I got an error on my calculator?

    • 2 years ago
  26. NotTim
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    Useless its tanx (as an entirety) that I using....

    • 2 years ago
  27. LagrangeSon678
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    Your trying to plug number right into the equation?

    • 2 years ago
  28. myininaya
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    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

    • 2 years ago
  29. NotTim
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    Lagrange, yes...

    • 2 years ago
  30. NotTim
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    Not the right idea huh?

    • 2 years ago
  31. FoolForMath
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    You need to NotThink a bit.

    • 2 years ago
  32. NotTim
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    ...ok? I do that a lot.

    • 2 years ago
  33. LagrangeSon678
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    Follow those steps that myin showed, youll end with the right answers

    • 2 years ago
  34. NotTim
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    I'm just looking at this and my notes, and I have not a clue.

    • 2 years ago
  35. NotTim
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    Is u=tanx?

    • 2 years ago
  36. myininaya
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    yes

    • 2 years ago
  37. NotTim
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    Ok.

    • 2 years ago
  38. FoolForMath
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    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 ..

    • 2 years ago
  39. NotTim
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    ERkk.

    • 2 years ago
  40. NotTim
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    Imma do this slowly... If yo ugotta do something while you help me, do it now as I work this thru...

    • 2 years ago
  41. NotTim
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    IS factor Thereom involved?

    • 2 years ago
  42. PaxPolaris
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    yes...if u-2 is a factor of P(u) ...P(2)=0

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

    • 2 years ago
  44. NotTim
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    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/.

    • 2 years ago
  45. NotTim
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    Sorry about that. My internet went wonky.

    • 2 years ago
  46. NotTim
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    And now I divide the thing by u-2 right?

    • 2 years ago
  47. myininaya
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    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

    • 2 years ago
  48. NotTim
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    ok

    • 2 years ago
  49. myininaya
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    pax did i make a mistake?

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

    • 2 years ago
  51. FoolForMath
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    myininaya, I wish If I can give you more medals for your patience.

    • 2 years ago
  52. NotTim
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    Lol.

    • 2 years ago
  53. myininaya
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    are you talking about me and my division above? lol

    • 2 years ago
  54. NotTim
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    I think just waiting for me to finish up my stuff here. Thanks by the way.

    • 2 years ago
  55. myininaya
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    oh i had a thing i was doing lol

    • 2 years ago
  56. PaxPolaris
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    sorry u r right. it's +3

    • 2 years ago
  57. NotTim
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    ITs +3?

    • 2 years ago
  58. myininaya
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    just making sure when it gets late i tend to screw up on little things

    • 2 years ago
  59. myininaya
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    like sometimes i don't know how to add or multiply sometimes

    • 2 years ago
  60. myininaya
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    we were talking about this: \[\left( u-2 \right)\left( u^2 - 7u +3\right) =0 \]

    • 2 years ago
  61. NotTim
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    ok. that scared me for a sec.

    • 2 years ago
  62. FoolForMath
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    yep myininaya I was talking about that :D

    • 2 years ago
  63. myininaya
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    lol

    • 2 years ago
  64. myininaya
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    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

    • 2 years ago
  65. NotTim
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    Finally, I'm done the division.

    • 2 years ago
  66. myininaya
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    lol

    • 2 years ago
  67. myininaya
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    good

    • 2 years ago
  68. myininaya
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    you have \[u-2=0 \text{ or } u^2-7u+3=0\]

    • 2 years ago
  69. myininaya
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    we need to use the quadratic formula to solve the second equation

    • 2 years ago
  70. NotTim
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    I hope I remember this for the test.

    • 2 years ago
  71. myininaya
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    so this is trig class?

    • 2 years ago
  72. myininaya
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    i could be wrong but this is too long to put on a test

    • 2 years ago
  73. myininaya
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    there might be a similar problem he/she puts there

    • 2 years ago
  74. myininaya
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    but shorter

    • 2 years ago
  75. NotTim
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    Whoops. I didn't type that...Double post or something.

    • 2 years ago
  76. myininaya
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    i could be wrong

    • 2 years ago
  77. LagrangeSon678
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    sometimes teachers get problems from special books

    • 2 years ago
  78. myininaya
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    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.

    • 2 years ago
  79. NotTim
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    K. Thanks man.

    • 2 years ago
  80. myininaya
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    Do I look like a man to you?

    • 2 years ago
  81. myininaya
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    Please say no

    • 2 years ago
  82. myininaya
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    lol

    • 2 years ago
  83. NotTim
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    Are you?

    • 2 years ago
  84. NotTim
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    I actually have bad vision and human identification problems.

    • 2 years ago
  85. NotTim
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    When I'm walking around I will misidentify everyone as the same person.

    • 2 years ago
  86. myininaya
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    Ok. Its cool. No worries.

    • 2 years ago
  87. NotTim
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    any1 know what I should do at (m-2)(m^2-7m+3)?

    • 2 years ago
  88. NotTim
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    For m^2-7m+3, do I have to do the quadratic formula?

    • 2 years ago
  89. NotTim
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    I guess I already know what to do with m-2, so I'm fine there.

    • 2 years ago
  90. NotTim
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    ERm, are you people just gunna lurk there? It's fine, just....

    • 2 years ago
  91. ktklown
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    find all places that u can be 0, then, recalling that u = tanx, solve for x.

    • 2 years ago
  92. ktklown
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    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.

    • 2 years ago
  93. NotTim
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    Ok.

    • 2 years ago
  94. NotTim
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    Hey, if one of my answers is 6.54, and I wanna get the other angle with it, what do i Do?

    • 2 years ago
  95. NotTim
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    Hi?

    • 2 years ago
  96. NotTim
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    Um, sorry if I sound abrupt, but could anyone please answer my most recent question?

    • 2 years ago
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