Question

whats an example of a non-extranious solution?

Answer 1

@jim_thompson5910

Answer 2

Do you know what an extraneous solution is?

Answer 3

kinda im just look for a radical equation that has a non extranious solution like an example and steps

Answer 4

let's say we had the equation

sqrt(x) = -1

Answer 5

what is the solution to that equation?

Answer 6

uhh would it be -1

Answer 7

but the square root of a negative number isn't a real number

ie

sqrt(-1) = a complex number (not a real number)

Answer 8

how would you isolate x

Answer 9

i dont know can you tell me (:

Answer 10

well we have x buried in a square root

we need to undo the square root to eliminate it and isolate x

Answer 11

what undoes square rooting?

Answer 12

by sqaureing a number

Answer 13

good

Answer 14

so we square both sides of

sqrt(x) = -1

to get

x = 1

Answer 15

notice how squaring -1 gives us

(-1)^2 = (-1)*(-1) = 1

Answer 16

so the possible solution to sqrt(x) = -1 is x = 1

Answer 17

however, we always should check the possible solutions

sqrt(x) = -1

sqrt(1) = -1 ... replace x with 1

1 = -1 ... this is false, so x = 1 is NOT a true solution

Answer 18

so we call x = 1 an extraneous solution

it popped up in the process of solving for x, but it's not a true solution to the *original* equation

Answer 19

oh ok so no im confused i was looking for a non-extranious

Answer 20

I know. I'm setting things up and defining what an extraneous solution is.

Answer 21

oh ok so now i understand the extranous way now i need to understand the non extranous

Answer 22

now if we made the right side positive, say +4, then we'll have this equation

sqrt(x) = 4

squaring both sides gives you x = 16

so the *possible* solution to sqrt(x) = 4 is x = 16

we always need to check things though


sqrt(x) = 4

sqrt(16) = 4 ... replace all copies of x with 16, the supposed solution

4 = 4 ... this equation is true


Because x = 16 satisfies the *original* equation, this confirms x = 16 to be a true solution to sqrt(x) = 4. So x = 16 is considered non-extraneous

Answer 23

extraneous solutions don't satisfy the original equation

non-extraneous solutions do satisfy the original equation

both are generated in the process of solving for x

Answer 24

ohhh ok now i get it. ok thank you for explaing so well (:

Answer 25

you're welcome