Question

Sat.

Answer 1

\[\sqrt{9x+81}=x+5\]And
\[9x+81 = (x+5)^2\]
what's the difference?

Answer 2

? one is the square of the other

Answer 3

no, but try that in wolf. you willl get different answers.

Answer 4

that is because they are different

Answer 5

how?

Answer 6

well because if for example i know x = 5, then i know x^2=25
but if i know x^2=25 then i don't know that x = 5

Answer 7

because of course it could be x = -5

Answer 8

right, but the confusion is that in which one i get 2 answers?

Answer 9

so just because one square is equal to another, it doesn't mean you started with the same thing. when you square both sides of an equation you can introduce a solution that was not in the original equation

Answer 10

so in sqrt one, i get 2 solutions? right?

Answer 11

there are two solutions to
\[9x+81=(x+5)^2\]

Answer 12

why not to the first one?

Answer 13

\[x=-8,x=7\] but only one solution to
\[\sqrt{9x+81}=x+5\]

Answer 14

why not for the first one?

Answer 15

well you can see that
\[x=-8\] does not work

Answer 16

Oh i seee. Now i get that... thanks man!

Answer 17

and you can even see why. if you replace x by -8 you get
\[\sqrt{9}=-3\] i.e.
\[3=-3\] which is false, but if you square both sides you get
\[9=9\] which is true

Answer 18

THanks.
one more question.

Answer 19

yw

Answer 20

what's the deal with:

\[\Huge \sqrt[12]{(-9)^{12}}\]

Answer 21

when you raise to an even power it is positive, so you get 9 as your answer

Answer 22

\[\Huge \sqrt[13]{(-9)^{13}}\]Now?

Answer 23

-9"

Answer 24

?

Answer 25

yes

Answer 26

so the deal lies with even numbers....

Answer 27

if the exponent is even then you will get a positive number

Answer 28

ok, thanks. now can you please come and see the question just above this one? pixie's question.

Answer 29

ok, i think i just added a comment to that one