## anonymous one year ago can someone explain to me how my teacher got this answer? its using substitution. Will give medals! give me one sec to post the problem

1. anonymous

$x^{1/2}+3x^{-1/2}-54x^{-3/2}=0$

2. anonymous

solve for x

3. anonymous

$\sqrt{x}+\frac{ 3 }{ \sqrt{x} }-\frac{ 54 }{ \left( \sqrt{x} \right)^3 }=0$ $put~\sqrt{x}=t$ $t+\frac{ 3 }{ t }-\frac{ 54 }{ t^3 }=0$ $multiply~ by ~t^3$ $t^4+3t^2-54=0$ put t^2=y $y^2+3y-54=0$ $y^2+9y-6y-54=0$ y=? then t=? x=?

4. anonymous

my teacher told us to try it like this: @surjithayer

5. anonymous

i dont understand the way he showed us in the above file

6. Nnesha

yea i was abt to solve like ^^that (Factor )

7. anonymous

where did the y come from?

8. anonymous

our teacher wants us to factor it

9. anonymous

i just dont get how he pulled out that exponential fraction

10. Nnesha

but i also like the way surjithayer's solved

11. anonymous

i need to learn how to factor out the negative exponent :(

12. Nnesha

he supposed that t^2 = y

13. Nnesha

so t^4 is same as t^2 times t^2 replace t^2 with y y times y = y^2 :=)

14. anonymous

i know how to use the substitution method, im just a little confused with how x^-1/2 was fatored out.

15. Nnesha

x^{-1/2) or x^{-3/2} ?

16. anonymous

x^-3/2, sorry

17. Nnesha

what's the lowest exponent of x ? that would be your common factor

18. Nnesha

wait i'll give you an example 2x^2+3x <--x^1 degree would be common factor

19. anonymous

okay gotcha

20. Nnesha

so what is common factor in ur equation ?

21. anonymous

x^-3/2, ause its the smallest

22. Nnesha

yes right!$\huge\rm x^\frac{ 1 }{ 2 }+ 3x^\frac{ -1 }{ 2}+54x^\frac{ -3 }{ 2 }$ take out the common factor when you take out x^{-3/2} from x^{1/2} what will ou have left ?$x^\frac{ -3 }{ 2}(??????????????)$

23. anonymous

i dont know

24. Nnesha

in other words divide all 3 terms by common factor $\huge\rm \frac{ x^\frac{ 1 }{ 2 } }{ x^\frac{ -3 }{ 2 } }+\frac{ 3x^\frac{ -1 }{ 2 } }{ x^\frac{ -3 }{ 2 } }+\frac{ 54x^\frac{ -3 }{ 2 } }{ x^\frac{ -3 }{ 2 }}$

25. Nnesha

remember when we divide same bases we should subtract their exponents (exponent rule) $\huge\rm \frac{ x^m }{ x^n }=x^{m-n}$

26. anonymous

^ thats ringing a bell

27. Nnesha

:P

28. Nnesha

example $\huge\rm \frac{ x^2 }{ x^1}=x^{2-1}$

29. anonymous

thats making such more sense

30. Nnesha

$\huge\rm \color{ReD}{ \frac{ x^\frac{ 1 }{ 2 } }{ x^\frac{ -3 }{ 2 } }}+\frac{ 3x^\frac{ -1 }{ 2 } }{ x^\frac{ -3 }{ 2 } }+\frac{ 54x^\frac{ -3 }{ 2 } }{ x^\frac{ -3 }{ 2 }}$ look at first term bases are the same so subtract their exponents $\huge\rm \color{Red}{x^{\frac{ 1 }{ 2 }-(\frac{ -3 }{ 2 })}}$

31. anonymous

i think i get it now, ou have to diivide all by it, that reduces it to the ax^2+bx+c

32. Nnesha

ye!!!

33. anonymous

wow youre good, thanks!!!!

34. Nnesha

$\huge\rm x^\frac{ -3 }{ 2 }(????+???+??)$ write ur answer in the parentheses

35. anonymous

(x^2+3x-54)

36. Nnesha

yep right!

37. anonymous

ive got it from this point out. shew you have no idea how long ive been trying to decifer this shenninagans!

38. Nnesha

aww se now you got it! great job!

39. anonymous

thank you so much