Question

Solve for x, given the equation Square root of x minus 5 + 7 = 11

Answer 1

\[\sqrt{x - 5} + 7 = 11\]

Answer 2

x = 21, solution is extraneous

x = 21, solution is not extraneous

x = 81, solution is extraneous

x = 81, solution is not extraneous

Answer 3

1) First subtract 7 on both sides.
2) Then square both sides..

Answer 4

3) Then add 5 on both sides.

Answer 5

I subtract the other 7 from 5 or 11?

Answer 6

11 right?

Answer 7

subtract 7 from 11.. 11-7

Answer 8

x = 9

Answer 9

would the x be square root still?

Answer 10

(x-5) ^0.5 = 11-7

(x-5)^0.5 = 4
now square both sides

(x-5) = 4^2

Answer 11

ohh yeah I forgot to square ughh sorry

Answer 12

no problem.

Answer 13

how do I square it?

Answer 14

square both side\(\Large \tt\color{blueviolet}{(\sqrt{x-5})^2=4^2\\ x-5=16}\)

Answer 15

solve for x now

Answer 16

x - 25 = 16? @xapproachesinfinity

Answer 17

why x-25? how did you come with that

Answer 18

you just need to add 5 to both side
this linear equation now?

Answer 19

ohh I hasd ssquare rooted it

Answer 20

x-5=16
5 5
_______________
x=21

Answer 21

No! square root with the square power cancel

Answer 22

ugh! Sorry, now how do I find out if its extraneous or not?

Answer 23

i'm not sure i understand what you meant?
you were looking for x and you got the solution?

Answer 24

I know but the choices are x = 21 is extraneous and x = 21, solution is not extraneous @xapproachesinfinity

Answer 25

It is ..

Answer 26

Its wrong

Answer 27

what does that mean by the way
never heard such a thing ??

Answer 28

@xapproachesinfinity google it :P :P

Answer 29

now i got it^_^
i google it actually
okay you answer is it not extraneous
the reason is 21 was included in the domain of the equation
to know if this is true
do this x-5>=0
x>5
so all real number that are greater than or equal to 5 therefore
21 was included
this thing is simple
when you solve watch out for the domain
especially the rational expression logarithm and such

Answer 30

@_angeliquexoxo it is good to know how to do this for next time
so watch the domain^_^

Answer 31

fyi, an extraneous solution is an "answer" you get after doing the algebra (correctly, of course), but when you put the answer into the original problem, *it does not work*

however, in this case, if we put 21 into your problem (i.e. replace x with 21)
and simplify we get
\[ \sqrt{21-5}+7 \\ \sqrt{16}+7 \\ 4+7\\11 \]

which matches the right-hand side.
in other words, 21 "works" so it is *not extraneous*

Answer 32

oh okay thankyou for the explanation! (: @phi

Answer 33

the English (not math) definition of extraneous is
Inessential or unrelated to the topic or matter at hand; irrelevant.

which might help you to remember what the "math" definition means