## 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)

1. MoreForJoe

how would you go about with the negative exponents?

2. Arnab09

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

3. MoreForJoe

then how would you get rid of fractions?

4. Arnab09

$(2\pm 2\sqrt{2}i)/3$

5. MoreForJoe

how'd you get that..?

6. Arnab09

solving the equation... :D

7. MoreForJoe

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

8. Arnab09

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

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

10. Arnab09

cross multiplication..

11. Dalvoron

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

12. yajjnobee

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

13. MoreForJoe

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

14. Dalvoron

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

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

16. Dalvoron

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

17. MoreForJoe

2/3,-2

18. Dalvoron

Correct, good job!

19. MoreForJoe

THANKS :D

20. MoreForJoe

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