Question

How do you solve this equation?

Answer 1

\[\sqrt{x-98}+2=1\]

I know the answer is extraneous, but I'm not sure how to get that.

Thanks so much!

Answer 2

we start by moving the 2 over to the RHS

sqrt(x-98) = -1

what do you think is next?

Answer 3

I think you square both sides?

Answer 4

yes and what would you get?

Answer 5

I think\[\left( \sqrt{x-98} \right)^{2} = (-1)^{2}\]

Answer 6

Or, after simplifying, ... what...?

Answer 7

from here we get x - 98 = 1

then solve for x

Answer 8

Oh yeah, that's what I got, too... Lol

Answer 9

Uhm, how do you solve for x now?

Answer 10

We want x isolated (alone) on the left side of the equation. So, think of what to do with that -98.

Answer 11

just add 98 to both sides

Answer 12

You add 98 to both sides.

Answer 13

So x = 1 + 98?

Answer 14

yes therefore x = 99

Answer 15

Now that you've gotten this tentative solution, why not substitute it back into the original equation as a check?

Answer 16

Okay! Thanks a lot! I don't know who to give a medal to now

Answer 17

Okay, give me a sec

Answer 18

to check put x=99 into your original equation

Answer 19

Caution: Unless the original equation is true with x = 99 substituted, either there is no solution or we've erred along the way.

Answer 20

Yeah, there is no solution

Answer 21

This sort of result (no solution) is entirely possible.

Answer 22

Hey I have one question about this: The first step where you move 2 over and get -1, is it -1 because +2 - 1 = -1?

Answer 23

A better reason would be that "we need to isolate the square root on the left side of the equation that involves the unknown, x."

Answer 24

Moving the 2 to the right hand side of the equation, by subtracting 2 from each side, accomplishes this.

Answer 25

Okay, I've got it. Thanks again!

Answer 26

My great pleasure. Good going.

Answer 27

@mathmale Hey can you tell me if I did this right? I have to show my work and it looks wrong.

sqrt x - 98 +2 = 1
sqrt x - 98 = -1
x - 98 = 1
x = 1 + 98
x = 99

sqrt 99 - 98 + 2 = 1
sqrt 99 - 98 = -1
99 - 98 = 1
99 = 1 + 98
99 = 99

Answer 28

Hey, HHS,
It's it's very important that you enclose that x - 98 in parentheses: sqrt(x-98). If you'll work through the problem again, you'll most likely end up where we did before: "no solution." Let me know if you have further questions.

Answer 29

Sorry, I'm not totally sure what you mean.

Answer 30

Sqrt(x-98) + 2 = 1
Sqrt(x-98) = -1
Square both sides.
x-98 = 1
x = 99.

Check: Sqrt(99-98) + 2 = ?? = 1
Sqrt(99-98) = ?? = -1
Sqrt(1) = ?? = -1

Sqrt(1) is generally taken to be +1.
Sqrt(1) = 1 is not equal to -1. Similarly, Sqrt(1) + 2 is not equal to 1.

Perhaps someone else could shed more light on the conclusion or conclusions we could arrive at.

Answer 31

Upon further thought: If we start out with Sqrt(x-98) + 2 = 1, there is NO x value that would result in Sqrt(x-98) taking on a negative value. I believe Sqrt(x-98) should be and is taken as the POSITIVE square root of (x-98) (called "the principal root"). Conclusion: no solution to the given problem.

Answer 32

Alright that makes sense. For your check, I don't really get why the question marks are there, and what could I put there? Because I don't think my teacher would be okay with question marks lol.

Thanks again.

Answer 33

The answer i gave originally is correct x=99 !!

because, if we substitute x=99 in sqrt(x-98) we get

sqrt(99 - 98) = sqrt1

Now the square root of 1 has two possible results +1 and -1

so in this case we just choose -1 and the LHS = -1 + 2 = 1

which is equal to the RHS. a mathematically valid result

so x = 99 is the solution !!

Answer 34

While you (alekos) are correct in stating that the Sqrt of 1 could be either (-) or (+), my stand is that substituting x=99 into the original equation must result in a mathematical statement that is true as is (without further manipulation) for x=99 to be a solution.

If we take the principal (+) square root of 1, the resulting equation, 1 + 2 = 1, is false.

Answer 35

I disagree

Answer 36

Great to live in a country where people can disagree openly and safely. Many thanks for sharing your views on this particular math question.

Answer 37

I agree with that :) always good to see the other man's point of view.