Question

Stephanie is student teaching at her local high school. She has to help her instructor write a test. She has to write a radical equation where the solution is extraneous. She also has to write a radical equation where the solution is non-extraneous. Help Stephanie write one radical equation where the solution is extraneous and another equation where the solution is non-extraneous. Using complete sentences, explain each step when solving to justify your examples. @satellite73 @iambatman @ganeshie8 @myininaya @Callisto @wio @Kainui @sammixboo

Answer 1

do they have to be hard?

Answer 2

no

Answer 3

as easy as possible please

Answer 4

then make it easy
take some sort of radical expression, anything, and set it equal to a negative number
for example
\[\sqrt{x-1}=-2\]

Answer 5

then what do i do?

Answer 6

it will have no solution
if you want to be trickier you can use \(\sqrt{x-1}+2=0\) same thing

Answer 7

well i need one that the solution will be extraneous and one that would be non extraneous

Answer 8

\[\sqrt{x-1}+2=0\] will have an "extraneous" solution

Answer 9

you can to solve it with
\[\sqrt{x-1}+2=0\\
\sqrt{x-1}=-2\] square and get
\[x-1=4\] so \[x=5\]
but if you check \(x=5\) it will not work

Answer 10

so its an extraneous solution?

Answer 11

yes it is extraneous whatever that means

Answer 12

the reason that did not work is because we had
\[\sqrt{x-1}=-2\] a negative number
if you make the right hand side a positive number it will work
you could even use
\[\sqrt{x-1}=2\]or something else more imaginative

Answer 13

thank you so much

Answer 14

yw