MoreForJoe
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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MoreForJoe
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how would you go about with the negative exponents?
Arnab09
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x^(-n)=1/(x^n)
MoreForJoe
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then how would you get rid of fractions?
Arnab09
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\[(2\pm 2\sqrt{2}i)/3\]
MoreForJoe
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how'd you get that..?
Arnab09
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solving the equation... :D
MoreForJoe
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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
Arnab09
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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 :)
MoreForJoe
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ok so i got to the (1-x)/x^2=3/4 what do i do next? O.o
Arnab09
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cross multiplication..
Dalvoron
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\[x^{-2}-x^{-1}=(3/4)\]\[\Leftrightarrow\frac{1}{x^2}-\frac{1}{x}=\frac{3}{4}\]
yajjnobee
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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:)
MoreForJoe
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am i supposed to get \[1\pm \sqrt{2}i/2\]?
Dalvoron
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No need for complex numbers here.\[\frac{1}{x^2}-\frac{1}{x}=\frac{3}{4}\]\[\Leftrightarrow \frac{4}{x^2}-\frac{4}{x}=3\]\[\Leftrightarrow 4-4x=3x^2\]
MoreForJoe
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thanks! i just use the quadratic formula and then get both answers :D
Dalvoron
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Quite right, quite right. Regular factorising is possible also. What did you get as your solutions for x?
MoreForJoe
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2/3,-2
Dalvoron
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Correct, good job!
MoreForJoe
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THANKS :D
MoreForJoe
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i have a few more problem that i cant get -.-