## dtan5457 one year ago If x+1/x=7, compute x^3+1/x^2

1. dtan5457

So far I have x^2+1=7x x^2=7x-1 x^3+1/7x-1 x^2x/(1)+1/(7x-1) when I cross out 7x-1 i get x+1. then what?

2. dtan5457

@Hero

3. Hero

Hang on a min.

4. dtan5457

okay thanks

5. Hero

( x+1)/x=7 multiply both sides by × x +1 =7x Subtract × from both sides 1=6x x= 1/6

6. Hero

Plug × to other expression

7. dtan5457

wait so all my x^2+1=7x was incorrect?

8. Hero

. Is the original problem you posted correct as written?

9. dtan5457

$x+\frac{ 1 }{ x }=7, x^3+\frac{ 1 }{ x^2 }=?$

10. Hero

± see, Better you use later to post from now on.

11. Hero

latex *

12. dtan5457

okay

13. dtan5457

so does your solution still stand?

14. dtan5457

@jdoe0001

15. Hero

No, it doesn't

16. dtan5457

any ideas?

17. Hero

Calculate ( x +1/ x ) ^ 2 and (x+1 / x ) ^ 3 )

18. dtan5457

i dont get it sorry

19. dtan5457

one of my friends even said its unsolvable without quadratic formula but im pretty sure my teacher doesnt want a quadratic use

20. Hero

( x + 1 / x ) ^ 2 = 7^2

21. Hero

22. Hero

Expand the left side

23. dtan5457

$x^2+\frac{ 1 }{ x^2 }+x+\frac{ 1 }{ x^2 }$

24. Hero

That's not what I got

25. dtan5457

lol i give up, i'll ask my teacher tomorrow. thanks

26. Hero

You give up too easy.

27. dtan5457

Been working on 4 problems for about 2 hours, it's time too move on if I want decently sufficient sleep. I've been getting mixed answers and solutions so I'll just let my teacher explain.

28. dtan5457

it can be solved with the quadratic formula so I just used that. Not sure if that's what my teacher wants but i'll see.

29. Hero

Nope, it probably isn't. There's another way to solve that your teacher may be looking for.