Question

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

Answer 1

how would you go about with the negative exponents?

Answer 2

x^(-n)=1/(x^n)

Answer 3

then how would you get rid of fractions?

Answer 4

\[(2\pm 2\sqrt{2}i)/3\]

Answer 5

how'd you get that..?

Answer 6

solving the equation... :D

Answer 7

nice haha but im still confused on what to do after the x's are on the bottom part of the fractions

Answer 8

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 :)

Answer 9

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

Answer 10

cross multiplication..

Answer 11

\[x^{-2}-x^{-1}=(3/4)\]\[\Leftrightarrow\frac{1}{x^2}-\frac{1}{x}=\frac{3}{4}\]

Answer 12

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

Answer 13

am i supposed to get \[1\pm \sqrt{2}i/2\]?

Answer 14

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

Answer 15

thanks! i just use the quadratic formula and then get both answers :D

Answer 16

Quite right, quite right. Regular factorising is possible also. What did you get as your solutions for x?

Answer 17

2/3,-2

Answer 18

Correct, good job!

Answer 19

THANKS :D

Answer 20

i have a few more problem that i cant get -.-