Question

sqrt x - 98 + 8 = 20

Does this have an extraneous solution? Steps for solving please!

Answer 1

Looks like this : \[\sqrt{x - 98} + 8 = 20\]

Answer 2

@Yttrium

Answer 3

@Jack1 @austinL

Answer 4

Can you define extraneous solution?

Answer 5

@Yttrium "A solution of a simplified version of an equation that does not satisfy the original equation." - http://www.mathwords.com/e/extraneous_solution.htm

Answer 6

Okay. Now you know it's meaning. Can you tell me what to do first?

Answer 7

Honestly, I was poorly introduced to square roots so I was never taught the steps, though I'd assume you work outside the square root first?

Answer 8

Okay. What you actually need to do is to isolate the terms having square roots. So, what will happen in our given equation?

Answer 9

Subtract 8. We'll have \[\sqrt{x - 98} = 12\]

Answer 10

Correct. So what will happen next?

Answer 11

I assume we eliminate the 98 which would become this
\[\sqrt{x} = 110\]

Answer 12

Ooopss. You can not easily eliminate 98 there. You must square first the whole equation to cancel the sqrt sign and then do the transpose.

Answer 13

And how would I do that?

Answer 14

We have
\[\sqrt{x-98} = 12]\]
right?
So,
\[[\sqrt{x-98} = 12]^2\]
And this will give us
x-98 = 144

Answer 15

How does that work?! I don't even see how you squared the whole equation like that.

But as for what you showed me, we'd then work with the 98 and make it this :
\[x = 242\]

Answer 16

It's just like \[[\sqrt{x-98}]=(12)^2\]
Yes. So, that will be the answer. And through substitution, you can chekc whether it is extraneous or not. :)

Answer 17

Hmm.. now I have that in my notes.

As for the equation, it wouldn't be extraneous since we have a solution, correct?

Answer 18

@Yttrium

Answer 19

Yes! :)

Answer 20

Alright thanks!

Answer 21

No prob. :))

Answer 22

Hope, you understand now. It's a pleasure for me. :))