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

1. MoreForJoe Group Title

how would you go about with the negative exponents?

2. Arnab09 Group Title

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

3. MoreForJoe Group Title

then how would you get rid of fractions?

4. Arnab09 Group Title

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

5. MoreForJoe Group Title

how'd you get that..?

6. Arnab09 Group Title

solving the equation... :D

7. MoreForJoe Group Title

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

8. Arnab09 Group Title

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 Group Title

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

10. Arnab09 Group Title

cross multiplication..

11. Dalvoron Group Title

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

12. yajjnobee Group Title

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

13. MoreForJoe Group Title

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

14. Dalvoron Group Title

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 Group Title

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

16. Dalvoron Group Title

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

17. MoreForJoe Group Title

2/3,-2

18. Dalvoron Group Title

Correct, good job!

19. MoreForJoe Group Title

THANKS :D

20. MoreForJoe Group Title

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