## anonymous one year ago PLEASE HELP NOT QUITE SURE ON THIS QUESTION Given the equation −4Square root of x minus 3 = 12, solve for x and identify if it is an extraneous solution.

1. anonymous

this is the equation: $\sqrt[-4]{x-3} = 12$

2. Nnesha

$\huge\rm -4\sqrt{x-3}=12$ first move the -4 to the right side

3. Nnesha

it's not 4th root right ? is it -4 (sqrt{x-3} ??

4. anonymous

yes you have it right

5. anonymous

@Nnesha @imqwerty

6. Nnesha

okay then first move the -4 to the right side how would do that ? divide , multiply add , or subtract ?

7. anonymous

8. anonymous

@Nnesha

9. Nnesha

now it's -4 times sqrt{x-3} what is opposite of multiplication ?

10. anonymous

division

11. Nnesha

yes right so divide both side by -4

12. anonymous

x-3=-2?

13. Nnesha

12/-4 = ??

14. anonymous

-3

15. Nnesha

$\sqrt{x-3}=-3$ now take square both sides to cancel out the square root

16. anonymous

so it would be 0

17. Nnesha

how ??

18. anonymous

wait no -9

19. anonymous

sorry

20. anonymous

x-3=-9

21. Nnesha

$\huge\rm (\sqrt{x-3})^2=(-3)^2$ when you take even power of NEGATIVE you will ALAWAYS get positive answer

22. anonymous

oh okay

23. Nnesha

sp (-3)^2 =? it's same as -3 times -3

24. anonymous

positive 9

25. Nnesha

x-3= 9 solve for x

26. anonymous

and then you would add 3 to get positive 12

27. anonymous

and then would it be extraneous or not extraneous?

28. Nnesha

okay to check if it's extraneous or not substitute x for 12 in the original equation

29. Nnesha

if both sides are equal then 12 isn't extraneous

30. anonymous

both sides came out equal so its not extraneous

31. Nnesha

how did you get equal sides ?

32. anonymous

honestly i don't know

33. Nnesha

$-4\sqrt{12-3}=12$ now solve

34. Nnesha

show me how did you do it ?

35. anonymous

ok

36. anonymous

im not sure how i did it but could you show me how to do it the right way please?

37. anonymous

i just guessed because i wasn't sure how to do it, the 4 on the outside of the sqr root confuses me

38. Nnesha

okay so we replaced x with 12 right now solve $-4\sqrt{12-3}=12$ 12-3 and then take square root

39. Nnesha

seee i knew it remember it's not 4 it's -4

40. Nnesha

hint: $-1\cancel{=}1$

41. anonymous

i got $\sqrt[16]{9} =12$

42. anonymous

that 16 isnt an exponent

43. Nnesha

hmm how did you get 16? 12-3 = ??

44. anonymous

i did -4^2

45. Nnesha

don't take square $-4\sqrt{12-3}$ you should substitute x for 12 into the original equation

46. Nnesha

12-3= 9 right $-4\sqrt{9}$ now solve

47. anonymous

equals -12

48. Nnesha

yes so -12 =12 ?

49. anonymous

sorry as you can tell i struggle with algebra

50. anonymous

no so they are extraneous

51. anonymous

the solution is not extraneous

52. anonymous

solution is extraneous right ? @Nnesha

53. Nnesha

which one is it extraneous or not ? like i said if you get equal sides THEN 12 is not extraneous

54. Nnesha

-12=12 both sides are equal ?

55. anonymous

no they are not equal so it is extraneous

56. Nnesha

yes right

57. anonymous

thanks so much for all your help that took awhile but thank you

58. Nnesha

my pleasure. :=)