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MoreForJoe

  • 3 years ago

solve the equation in the set of complex numbers. give only exact answers, not approximations... x^(-2)-x^(-1)=(3/4)

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  1. MoreForJoe
    • 3 years ago
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    how would you go about with the negative exponents?

  2. Arnab09
    • 3 years ago
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    x^(-n)=1/(x^n)

  3. MoreForJoe
    • 3 years ago
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    then how would you get rid of fractions?

  4. Arnab09
    • 3 years ago
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    \[(2\pm 2\sqrt{2}i)/3\]

  5. MoreForJoe
    • 3 years ago
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    how'd you get that..?

  6. Arnab09
    • 3 years ago
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    solving the equation... :D

  7. MoreForJoe
    • 3 years ago
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    nice haha but im still confused on what to do after the x's are on the bottom part of the fractions

  8. Arnab09
    • 3 years ago
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    make the bottom part x^2 u will get like this: (1-x)/x^2=3/4 after cross multiplication, u can get a quadratic expression, solve that u will get the answer :)

  9. MoreForJoe
    • 3 years ago
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    ok so i got to the (1-x)/x^2=3/4 what do i do next? O.o

  10. Arnab09
    • 3 years ago
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    cross multiplication..

  11. Dalvoron
    • 3 years ago
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    \[x^{-2}-x^{-1}=(3/4)\]\[\Leftrightarrow\frac{1}{x^2}-\frac{1}{x}=\frac{3}{4}\]

  12. yajjnobee
    • 3 years ago
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    agree with dalvoron. Crossed multiply it and get x-x^2=3/4. then transpose 3/4 to the other side:)

  13. MoreForJoe
    • 3 years ago
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    am i supposed to get \[1\pm \sqrt{2}i/2\]?

  14. Dalvoron
    • 3 years ago
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    No need for complex numbers here.\[\frac{1}{x^2}-\frac{1}{x}=\frac{3}{4}\]\[\Leftrightarrow \frac{4}{x^2}-\frac{4}{x}=3\]\[\Leftrightarrow 4-4x=3x^2\]

  15. MoreForJoe
    • 3 years ago
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    thanks! i just use the quadratic formula and then get both answers :D

  16. Dalvoron
    • 3 years ago
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    Quite right, quite right. Regular factorising is possible also. What did you get as your solutions for x?

  17. MoreForJoe
    • 3 years ago
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    2/3,-2

  18. Dalvoron
    • 3 years ago
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    Correct, good job!

  19. MoreForJoe
    • 3 years ago
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    THANKS :D

  20. MoreForJoe
    • 3 years ago
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    i have a few more problem that i cant get -.-

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