Question

please help!!
Task 2

Part 1. Create two radical equations: one that has an extraneous solution, and one that does not have an extraneous solution. Use the equation below as a model.

a√x+b +c=d

Use a constant in place of each variable a, b, c, and d. You can use positive and negative constants in your equation.

Part 2. Show your work in solving the equation. Include the work to check your solution and show that your solution is extraneous.

Part 3. Explain why the first equation has an extraneous solution and the second does not.

Answer 1

@ganeshie8

Answer 2

\[a\sqrt{x+b}+c=d\]

Answer 3

assign some numbers to a,b,c,d

Answer 4

any number?

Answer 5

for part a, you want the equation to have extraneous solution
so make \(d\) less than \(c\)

Answer 6

yes choose ur favorite numbers such that d is less than c

Answer 7

2,4,7,6

Answer 8

just to make the calculations much simpler, how about picking

1,4,7,6 ?

Answer 9

ok ya fine with me

Answer 10

\[1\sqrt{x+4}+7=6\]

solve \(x\)

Answer 11

start by subtracting 7 both sides

Answer 12

-5

Answer 13

doesn't look right, show ur work

Answer 14

I used a calculator for it

Answer 15

\[1\sqrt{x+4}+7=6\]

subtract 7 both sides, what do you get ?

Answer 16

you get : \[\sqrt{x+4}=-1\]

right ?

Answer 17

ya sorry my computer glitched

Answer 18

next square both sides so that radical disappears on left hand side :

\[x+4=1\]

Answer 19

isolate \(x\)

Answer 20

would it be 1? and this is for part one right?

Answer 21

how did you get 1 ?

Answer 22

you said to square it.

Answer 23

Ohk, next isolate x

Answer 24

how do u do that? sorry im not good at this

Answer 25

watch this short video
https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-expressions-and-variables/cc-6th-beginner-equations/v/solving-one-step-equations

Answer 26

-3

Answer 27

good, so x = -3 is what you get by solving
check if it really satisfies the given radical equation

Answer 28

plugin x=-3 in the equation
\[1\sqrt{x+4}+7=6\]

Answer 29

ok so I just input -3 into the radical equation and solve right

Answer 30

just input x=-3 into the radical equation and see if you get same thing on both sides

Answer 31

its not true its false

Answer 32

that means x=-3 is an extraneous solution

Answer 33

we're done with half of part a and part b

Answer 34

create another equation cleverly such that you dont get an extraneous solution

Answer 35

ok so for part a we have one equation and it does not have an extraneous solution am I right?

so I pick four more numbers?

Answer 36

the one we worked just now has an extraneous solution

Answer 37

yes pick four more numbers such that you DONT get an extraneous solution

Answer 38

oh ok and that equation was when I input the -3 in it? im just trying to understand

Answer 39

for the second equation without extranesou solution, you may simply exchange c and d

\[1\sqrt{x+4}+6=7\]

Answer 40

this equation should not give you extraneous solutions

Answer 41

start by subtracting 6 both sides

Answer 42

-1

Answer 43

sorry I mean 1 @ganeshie8

Answer 44

yes! square both sides and solve x all the way

Answer 45

I got -3

Answer 46

Yep!

Answer 47

plug that into the original equation and see if it satisfies

Answer 48

its true

Answer 49

that means the solution is NOT extraneous

Answer 50

we're done with part a and part b

Answer 51

ok just to get this straight the extraneous solution was