Question

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

Answer 1

\[x^{1/2}+3x^{-1/2}-54x^{-3/2}=0\]

Answer 2

solve for x

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

where did the y come from?

Answer 8

our teacher wants us to factor it

Answer 9

i just dont get how he pulled out that exponential fraction

Answer 10

but i also like the way surjithayer's solved

Answer 11

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

Answer 12

he supposed that t^2 = y

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

x^-3/2, sorry

Answer 17

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

Answer 18

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

Answer 19

okay gotcha

Answer 20

so what is common factor in ur equation ?

Answer 21

x^-3/2, ause its the smallest

Answer 22

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 ?\[x^\frac{ -3 }{ 2}(??????????????)\]

Answer 23

i dont know

Answer 24

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

Answer 25

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

Answer 26

^ thats ringing a bell

Answer 27

:P

Answer 28

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

Answer 29

thats making such more sense

Answer 30

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

Answer 31

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

Answer 32

ye!!!

Answer 33

wow youre good, thanks!!!!

Answer 34

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

Answer 35

(x^2+3x-54)

Answer 36

yep right!

Answer 37

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

Answer 38

aww se now you got it! great job!

Answer 39

thank you so much