Question

can someone please come up with a radical equation and check for an extraneous solution?(its not supposed to be extraneous)

Answer 1

set a square root equal to a positive number.

Answer 2

so like 2√(5)

Answer 3

@phi

Answer 4

you want an equation. that means
left side = right side

you also want a variable (call it x)

the idea is to write
square root ( some expression with x) = some positive number

Answer 5

oh and it has to model ax+b+c=d.

Answer 6

so 2√(5+4)+2=4

Answer 7

so 2√(5+4)+2=4

Answer 8

@phi

Answer 9

2√(5+4)+2=4
-2 -2
2 √(5+4)=4

Answer 10

2* sqrt 9=6

Answer 11

x=6?

Answer 12

change it to this
\[ 2\sqrt{(x+4)}+2=4\]
because you need an x

Answer 13

oh right

Answer 14

thank you

Answer 15

ill solve it

Answer 16

now subtract 2 from both sides
what do you get ?

Answer 17

2√(x+4)=2

Answer 18

do i have to multiply both sides by 2?

Answer 19

@phi

Answer 20

you want to "get rid" of the 2 in front of the square root
notice you have 2 times square root
to get rid of the 2, do the opposite of multiply (to both sides)

Answer 21

ah

Answer 22

in other words, divide both sides by 2
what do you get ?

Answer 23

√4=1

Answer 24

√x=4=1

Answer 25

√x+4=1

Answer 26

almost, you mean
\[ \sqrt{x+4 }=1\]

Answer 27

now square both sides

Answer 28

x+16=1?

Answer 29

if you have
\[ \sqrt{stuff}\]
and you square it, you get back stuff
you don't change what's inside ....
in other words, the only thing that changes is the square root "goes away"

Answer 30

x+4=1?

Answer 31

yes

Answer 32

-4 to both side

Answer 33

last step is add -4 to both sides

Answer 34

x=-3

Answer 35

add 4?

Answer 36

yes. and if you put x=-3 into the equation
\[ 2 \sqrt{x+4}= 2 \]
the left side will simplify to 2, show x=-3 is not extraneous

Answer 37

2√(-3+4)+2=2
2√(-3+4)=0

Answer 38

idk the next step

Answer 39

oh nvm

Answer 40

2√1=0

Answer 41

I put in the wrong original equation
you started with
\[ 2\sqrt{(x+4)}+2=4 \]

to show x=-3 "works" , replace x with -3, and simplify only the left side (leave the = 4 alone)

Answer 42

2√(-3+4)+2
2√(1)+2

Answer 43

yes, and order of operations says now do sqrt(1)

Answer 44

2

Answer 45

sqrt(1) means what times itself = 1

Answer 46

oh

Answer 47

sqrt(1)= 1 (notice 1 is special)

another example: sqrt(4) = 2 (because 2*2 is 4)

Answer 48

sqrt(1) is 1 because 1*1 is 1

Answer 49

i see

Answer 50

2√(1)+2
becomes
2*1 + 2

now order of operations: do the multiply next

Answer 51

2*1=1

Answer 52

2

Answer 53

I'm sorry 2*1 is 2

Answer 54

+2=4

Answer 55

nooooo

Answer 56

i mean yes

Answer 57

its not extraneous

Answer 58

thank you so much sir

Answer 59

yes, that is good
you just showed
\[ 2\sqrt{(x+4)}+2=4 \]
becomes
4=4
when x= -3
so x=-3 makes the equation true (left side equals right side)

Answer 60

Thank you, i just fanned u and gave you a medal and a testimonial

Answer 61

ive lerned more now than the past 2 months in algebra