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.

Answer 1

I made the non extraneous solution but the extraneous solution i'm getting confused about.

Answer 2

x^2+4=81

Answer 3

why negative?

Answer 4

sorry my computer is not cooperating

Answer 5

it's fine and x^2 and 4 are square roots

Answer 6

\[\sqrt{7x-1}+8=0\]

Answer 7

\[\sqrt{7x-1}+8=0\]

Answer 8

ok this one will work, let me explain

Answer 9

subtract 8 to both sides

Answer 10

square both sides

Answer 11

\[\sqrt{7x-1}=-8\]

Answer 12

7x-1=64

Answer 13

finish solving it

Answer 14

x=9

Answer 15

no

Answer 16

7x=65

Answer 17

7x-1=64
+1 +1
7x=65
divide 7 to both sides
x=65/7

Answer 18

ok now sub into original equation

Answer 19

sry i subtracted instead of added

Answer 20

no problem, test it

Answer 21

\[\pm 8 = 8\]

Answer 22

-8 i meant

Answer 23

no

Answer 24

\[\sqrt{7\left( \frac{ 65 }{ 7 } \right)-1}+8=0\]

Answer 25

\[\sqrt{65-1}+8=0\]
\[\sqrt{64}+8=0\]
8+8=0
16=0
false therefore solution is extraneous

Answer 26

oh, thx, may i have the original solution

Answer 27

x=65/7

Answer 28

ok use the one I left

Answer 29

And here's a medal

Answer 30

thanks hope that help you

Answer 31

You're welcome

Answer 32

May i ask is This an extraneous solution \[\sqrt{x}=3\]

Answer 33

no because the square root of 9 is 3 so x=9 is a solution

Answer 34

so it's non-extraneous

Answer 35

its a solution it is not extraneous
its either extraneous or a solution
extraneous-extra solution that is in error (it doesn't work)

Answer 36

Ok i was hoping for it to be non extraneous

Answer 37

non is not

Answer 38

i know