Question

Given the equation Square root of 8x plus 1 = 5, solve for x and identify if it is an extraneous solution.

A)x = One fourth, solution is not extraneous
B)x = One fourth, solution is extraneous
C)x = 3, solution is not extraneous
D)x = 3, solution is extraneous

Answer 1

\[\Large \sqrt{8x+1}=5\]
is this it?

Answer 2

yup

Answer 3

Well then, how do you go about solving for x?

Answer 4

would u square both sides to get the 8x out the square root?

Answer 5

Squaring both sides seems logical...what do you get? :)

Answer 6

(8x+1)^2 = 5^2
64x+1= 25?

Answer 7

I don't know if I did that right

Answer 8

Oh, okay, two things, first, and this is very important (though actually irrelevant to your problem)
\[\Large (8x+1)^2 \color{red}\ne 64x + 1\]
Do you remember FOIL?
\[\Large (8x+1)^2 = (8x+1)(8x+1)=64x^2 + 16x+1\]
But anyway, again, that's not relevant to this problem...
do recall that squaring and the *radical sign* cancel each other out... like so:
\[\Large (\sqrt a)^2=a\]

Answer 9

kinda

Answer 10

kinda?
When you put it that way, it isn't enough :P
\[\Large (\sqrt a)^2 = a\]\[\Large \left(\sqrt{8x+1}\right)^2 = \color{red}?\]

Answer 11

wouldnt it be 64x^2 + 16x +1, but what do I do after that

Answer 12

No, it won't :P
Look again at my previous post...
I said that thing involving 64x^2 + 16x + 1 has nothing to do with your current problem :)

Answer 13

so since they cancel itself outitd be just eithe just x or 8x+1

Answer 14

Which is it? ^_^
(Sorry for egging you, this is necessary for self-reliance...)

Answer 15

8x+1 :D

Answer 16

Keep in mind that for this to be the correct result, we MUST know that \(8x + 1 \ge 0\;or\; x \ge -1/8\). This is not an optional thing to know.

Answer 17

So after you do square both sides, you get...?

Answer 18

8x+1=25????

Answer 19

That's good. Now solve for x ^_^

Answer 20

x=3

Answer 21

Now you have a tentative value for x... is it extraneous, though? :)

Answer 22

It mustn't result in a radical that I like to call... 'illegal'.
Plug it into the radicand 8x+1 and make sure you get something that is not a negative number.... so, DO you get a negative number when you plug in x = 3 into the radicand?

Answer 23

no... and extraneous solution is a invalid solution right?

Answer 24

Yup... so your final answer is choice.... which choice? :)

Answer 25

C). x=3 not extraneous

Answer 26

i got it right on the test THANK YOU!

Answer 27

Well... that wasn't too hard, was it? ^_^

Good job.