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x3_drummerchick

  • one year ago

can someone explain to me how my teacher got this answer? its using substitution. Will give medals! give me one sec to post the problem

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  1. x3_drummerchick
    • one year ago
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    \[x^{1/2}+3x^{-1/2}-54x^{-3/2}=0\]

  2. x3_drummerchick
    • one year ago
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    solve for x

  3. anonymous
    • one year ago
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    \[\sqrt{x}+\frac{ 3 }{ \sqrt{x} }-\frac{ 54 }{ \left( \sqrt{x} \right)^3 }=0\] \[put~\sqrt{x}=t\] \[t+\frac{ 3 }{ t }-\frac{ 54 }{ t^3 }=0\] \[multiply~ by ~t^3\] \[t^4+3t^2-54=0\] put t^2=y \[y^2+3y-54=0\] \[y^2+9y-6y-54=0\] y=? then t=? x=?

  4. x3_drummerchick
    • one year ago
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    my teacher told us to try it like this: @surjithayer

  5. x3_drummerchick
    • one year ago
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    i dont understand the way he showed us in the above file

  6. Nnesha
    • one year ago
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    yea i was abt to solve like ^^that (Factor )

  7. x3_drummerchick
    • one year ago
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    where did the y come from?

  8. x3_drummerchick
    • one year ago
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    our teacher wants us to factor it

  9. x3_drummerchick
    • one year ago
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    i just dont get how he pulled out that exponential fraction

  10. Nnesha
    • one year ago
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    but i also like the way surjithayer's solved

  11. x3_drummerchick
    • one year ago
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    i need to learn how to factor out the negative exponent :(

  12. Nnesha
    • one year ago
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    he supposed that t^2 = y

  13. Nnesha
    • one year ago
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    so t^4 is same as t^2 times t^2 replace t^2 with y y times y = y^2 :=)

  14. x3_drummerchick
    • one year ago
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    i know how to use the substitution method, im just a little confused with how x^-1/2 was fatored out.

  15. Nnesha
    • one year ago
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    x^{-1/2) or x^{-3/2} ?

  16. x3_drummerchick
    • one year ago
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    x^-3/2, sorry

  17. Nnesha
    • one year ago
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    what's the lowest exponent of x ? that would be your common factor

  18. Nnesha
    • one year ago
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    wait i'll give you an example 2x^2+3x <--x^1 degree would be common factor

  19. x3_drummerchick
    • one year ago
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    okay gotcha

  20. Nnesha
    • one year ago
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    so what is common factor in ur equation ?

  21. x3_drummerchick
    • one year ago
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    x^-3/2, ause its the smallest

  22. Nnesha
    • one year ago
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    yes right!\[\huge\rm x^\frac{ 1 }{ 2 }+ 3x^\frac{ -1 }{ 2}+54x^\frac{ -3 }{ 2 }\] take out the common factor when you take out x^{-3/2} from x^{1/2} what will ou have left ?\[x^\frac{ -3 }{ 2}(??????????????)\]

  23. x3_drummerchick
    • one year ago
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    i dont know

  24. Nnesha
    • one year ago
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    in other words divide all 3 terms by common factor \[\huge\rm \frac{ x^\frac{ 1 }{ 2 } }{ x^\frac{ -3 }{ 2 } }+\frac{ 3x^\frac{ -1 }{ 2 } }{ x^\frac{ -3 }{ 2 } }+\frac{ 54x^\frac{ -3 }{ 2 } }{ x^\frac{ -3 }{ 2 }}\]

  25. Nnesha
    • one year ago
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    remember when we divide same bases we should `subtract `their exponents (exponent rule) \[ \huge\rm \frac{ x^m }{ x^n }=x^{m-n}\]

  26. x3_drummerchick
    • one year ago
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    ^ thats ringing a bell

  27. Nnesha
    • one year ago
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    :P

  28. Nnesha
    • one year ago
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    example \[\huge\rm \frac{ x^2 }{ x^1}=x^{2-1}\]

  29. x3_drummerchick
    • one year ago
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    thats making such more sense

  30. Nnesha
    • one year ago
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    \[\huge\rm \color{ReD}{ \frac{ x^\frac{ 1 }{ 2 } }{ x^\frac{ -3 }{ 2 } }}+\frac{ 3x^\frac{ -1 }{ 2 } }{ x^\frac{ -3 }{ 2 } }+\frac{ 54x^\frac{ -3 }{ 2 } }{ x^\frac{ -3 }{ 2 }}\] look at first term bases are the same so subtract their exponents \[\huge\rm \color{Red}{x^{\frac{ 1 }{ 2 }-(\frac{ -3 }{ 2 })}}\]

  31. x3_drummerchick
    • one year ago
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    i think i get it now, ou have to diivide all by it, that reduces it to the ax^2+bx+c

  32. Nnesha
    • one year ago
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    ye!!!

  33. x3_drummerchick
    • one year ago
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    wow youre good, thanks!!!!

  34. Nnesha
    • one year ago
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    \[\huge\rm x^\frac{ -3 }{ 2 }(????+???+??)\] write ur answer in the parentheses

  35. x3_drummerchick
    • one year ago
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    (x^2+3x-54)

  36. Nnesha
    • one year ago
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    yep right!

  37. x3_drummerchick
    • one year ago
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    ive got it from this point out. shew you have no idea how long ive been trying to decifer this shenninagans!

  38. Nnesha
    • one year ago
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    aww se now you got it! great job!

  39. x3_drummerchick
    • one year ago
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    thank you so much

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