Given the equation radical 8x+1 = 5, solve for x and identify if it is an extraneous solution.
a. x = 1/4 , solution is not extraneous
b. x =1/4 , solution is extraneous
c. x = 3, solution is not extraneous
d. x = 3, solution is extraneous

- anonymous

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- yamyam70

you mean \[\sqrt{8x +1}\] = 5 ?

- anonymous

Is it the question ?
\[sqrt{8x+1}\]=5
Please answer and get answer :)

- anonymous

@yamyam70 yes

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## More answers

- yamyam70

hello,
if a linear equation has a radical , square both sides :)

- anonymous

so it would be 64x+1=25

- yamyam70

\[(\sqrt{8x + 1} )^2 = (5)^2\]

- yamyam70

nope, by squaring both sides, take notice of the left hand side, we remove the radical.

- yamyam70

\[\sqrt{8x + 1 } \times \sqrt{8x +1} = 8x +1 \]

- anonymous

so the left side would stay 8x+1

- yamyam70

aha!

- yamyam70

so please continue, 8x + 1 = (5)^2 :)

- anonymous

x=3?

- yamyam70

How did you get that answer? :)

- anonymous

subtract 1 from each side then divide by 8.

- anonymous

what does extraneous solution mean?

- yamyam70

Correct! How would you tell if it is extraneous or not?

- anonymous

idk what that means.

- yamyam70

We check the equation, by substituting the value of x. :)

- anonymous

i got 5=5

- yamyam70

if you check it and the results of the left hand side is equal to the right hand side it is not extraneous :) if it does not equal , it is extraneous :)

- anonymous

oh ok thankyou!

- yamyam70

Welcome to open study! please read the code of conduct if you have time :)

- yamyam70

- yamyam70

you're welcome :)

- anonymous

another question!

- yamyam70

sure :)

- anonymous

Solve for x, given the equation \[\sqrt{x-5}+7=11\]
x = 21, solution is extraneous
x = 21, solution is not extraneous
x = 81, solution is extraneous
x = 81, solution is not extraneous

- yamyam70

I see
then same procedure, square both sides :)

- anonymous

x-5+49=121

- yamyam70

oh wait, 7 isn't involved

- yamyam70

one moment please

- anonymous

ok

- yamyam70

are you sure about the given choices?

- anonymous

yes i got 77 but that answer was not there

- yamyam70

I see, we got same, I'm trying a different approach, one moment

- anonymous

ok

- yamyam70

okay here goes,

- yamyam70

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

- yamyam70

we tranfer 7 to the right hand side :)

- yamyam70

what would we have?

- anonymous

\[\sqrt{x-5}=18\]

- anonymous

and then do we square both sides?

- yamyam70

wrong :) , when we tranfer 7 , we change the signs right? :)

- anonymous

yes the right side is supposed to be 4

- yamyam70

correct :) then we square both sides, the equation should look like \[\sqrt{x-5} = 4 \]

- anonymous

i got x= 17

- yamyam70

wrong :)
\[(\sqrt{x-5?})^2 = (4)\]

- yamyam70

(x−5?−−−−−√)2=(4)^2

- anonymous

do i foil them?

- yamyam70

wait nevermind that

- yamyam70

\[(\sqrt{x-5})^2=(4)^2\]

- yamyam70

^^^^^^ thats the correct one

- anonymous

so how to i solve for that?

- yamyam70

remember when we square , \[\sqrt{x-5}\] it will give us x-5 :)

- yamyam70

\[(\sqrt{x-5}) (\sqrt{x-5}) = x-5\]

- anonymous

x=21

- yamyam70

correct :) , so check if it is extraneous or not :)

- anonymous

it is not

- yamyam70

Correct :)

- anonymous

Given the equation \[\sqrt[-4]{x-3}=12\], solve for x and identify if it is an extraneous solution.
x = 0, solution is not extraneous
x = 0, solution is extraneous
x = 12, solution is not extraneous
x = 12, solution is extraneous

- yamyam70

is that -4 ?

- anonymous

yes

- anonymous

would it be this \[x-3\frac{ 1 }{ -4}=12\]

- yamyam70

hmm, I'm not quite sure about the rule here.

- yamyam70

I would suggest too start another session. :)

- yamyam70

I'm sorry , I can't help you with this one :)

- anonymous

ok thanks for the help

- yamyam70

Bye :)

- yamyam70

Don't forget to close the question :)

- anonymous

how do i do that?

- yamyam70

On the left side, there is a timer, "bump in" beside it click close. :)

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