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.

Question

jozelynw · Answer

How to make a extraneous solution?

jozelynw · Answer

@ikram002p

jozelynw · Answer

@welshfella

jozelynw · Answer

do you know how to write a extraneous radical equation

xapproachesinfinity · Answer

extraneous sol is  solution that is not in the domain of the equation you started with

jozelynw · Answer

huh

jozelynw · Answer

well, then how do I create a radical extraneous equation?

xapproachesinfinity · Answer

consider the following equation $\sqrt{\frac{x+1}{x}}=\sqrt{\frac{1}{x}}$
see that x=0 is not in the domain
try to solve that equation

xapproachesinfinity · Answer

it is easier to create an equation with correct solution (not extraneous )

welshfella · Answer

-3 sqrt(7 + 2x) = 24
sqrt(7 + 2x) = -8
square both sides
7 + 2x = 64
2x = 57
x = 57/2


now plug in x = 57/2 and see if it satisfies the original equation

xapproachesinfinity · Answer

consider the following equation $\sqrt{x+1}=\sqrt{3x-1}$
solution is $x=1$ if we check it on the equation we it checks out

jozelynw · Answer

it wants me to use this equation a√x+b+c=d

xapproachesinfinity · Answer

you just said radical equation you did specify any details

xapproachesinfinity · Answer

well at any rate check @welshfella work

jozelynw · Answer

I know because then you would just be giving me answers and then people would be thinking that im cheating

welshfella · Answer

a negative number times a radical will give an extraneous solution

jozelynw · Answer

so i just wanted to know how to create a radical extraneous equation

jozelynw · Answer

can you give me an example

welshfella · Answer

if you plug in 57/2 into the above it won't give you 24

jozelynw · Answer

but it's suppose to

jozelynw · Answer

28.5

welshfella · Answer

no  - ones like that will give an extraneous solution  When you square  you get a positive result so a negative value can get 'lost'.

jozelynw · Answer

so 28.5 is not 57/2

welshfella · Answer

-3 * sqrt(7 + 28.5) =  -17.87

jozelynw · Answer

what do you mean sqrt ? sqrt of 3

welshfella · Answer

do you see that this is an extraneous solution?

welshfella · Answer

square root of (7 + 28.5)

jozelynw · Answer

i do it equals -17.87

jozelynw · Answer

wait did something wrong

jozelynw · Answer

sqrt of 35.5 =5.95     and 5.95 times            -3 equals -17.87

welshfella · Answer

yes that is correct

so 28.5 is not a solution  its extraneous

welshfella · Answer

now one that does not have an extraneous solution would  be

sqrt(4x + 1)  = 7

so 
4x + 1 = 49
4x = 48
x = 12

which will fit the original equation

welshfella · Answer

here is a link which deals with the subject http://www.purplemath.com/modules/solverad2.htm

jozelynw · Answer

what are the options

welshfella · Answer

what do you mean?

jozelynw · Answer

you said " which will fit the original equation"

welshfella · Answer

I meant if you replace  x by 12 in the original equation then the equation will balance 

the left side will equal 7

welshfella · Answer

sqrt(4*12 + 1) = sqrt 49  = 7

welshfella · Answer

so x = 12 is a valid solution

jozelynw · Answer

so the rule to this is.......

welshfella · Answer

a negative value as above will give an extraneous solution. But there' more to it than that that's why i posted the link.  Some equations will have one valid and one extraneous solution , for example.

welshfella · Answer

sorry but i have to go now

jozelynw · Answer

thank you so much for you help @welshfella

welshfella · Answer

yw