anonymous
  • anonymous
can someone please come up with a radical equation and check for an extraneous solution?(its not supposed to be extraneous)
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
phi
  • phi
set a square root equal to a positive number.
anonymous
  • anonymous
so like 2√(5)
anonymous
  • anonymous
@phi

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

phi
  • phi
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
anonymous
  • anonymous
oh and it has to model ax+b+c=d.
anonymous
  • anonymous
so 2√(5+4)+2=4
anonymous
  • anonymous
so 2√(5+4)+2=4
anonymous
  • anonymous
@phi
anonymous
  • anonymous
2√(5+4)+2=4 -2 -2 2 √(5+4)=4
anonymous
  • anonymous
2* sqrt 9=6
anonymous
  • anonymous
x=6?
phi
  • phi
change it to this \[ 2\sqrt{(x+4)}+2=4\] because you need an x
anonymous
  • anonymous
oh right
anonymous
  • anonymous
thank you
anonymous
  • anonymous
ill solve it
phi
  • phi
now subtract 2 from both sides what do you get ?
anonymous
  • anonymous
2√(x+4)=2
anonymous
  • anonymous
do i have to multiply both sides by 2?
anonymous
  • anonymous
@phi
phi
  • phi
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)
anonymous
  • anonymous
ah
phi
  • phi
in other words, divide both sides by 2 what do you get ?
anonymous
  • anonymous
√4=1
anonymous
  • anonymous
√x=4=1
anonymous
  • anonymous
√x+4=1
phi
  • phi
almost, you mean \[ \sqrt{x+4 }=1\]
phi
  • phi
now square both sides
anonymous
  • anonymous
x+16=1?
phi
  • phi
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"
anonymous
  • anonymous
x+4=1?
phi
  • phi
yes
anonymous
  • anonymous
-4 to both side
phi
  • phi
last step is add -4 to both sides
anonymous
  • anonymous
x=-3
anonymous
  • anonymous
add 4?
phi
  • phi
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
anonymous
  • anonymous
2√(-3+4)+2=2 2√(-3+4)=0
anonymous
  • anonymous
idk the next step
anonymous
  • anonymous
oh nvm
anonymous
  • anonymous
2√1=0
phi
  • phi
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)
anonymous
  • anonymous
2√(-3+4)+2 2√(1)+2
phi
  • phi
yes, and order of operations says now do sqrt(1)
anonymous
  • anonymous
2
phi
  • phi
sqrt(1) means what times itself = 1
anonymous
  • anonymous
oh
phi
  • phi
sqrt(1)= 1 (notice 1 is special) another example: sqrt(4) = 2 (because 2*2 is 4)
phi
  • phi
sqrt(1) is 1 because 1*1 is 1
anonymous
  • anonymous
i see
phi
  • phi
2√(1)+2 becomes 2*1 + 2 now order of operations: do the multiply next
anonymous
  • anonymous
2*1=1
anonymous
  • anonymous
2
anonymous
  • anonymous
I'm sorry 2*1 is 2
anonymous
  • anonymous
+2=4
anonymous
  • anonymous
nooooo
anonymous
  • anonymous
i mean yes
anonymous
  • anonymous
its not extraneous
anonymous
  • anonymous
thank you so much sir
phi
  • phi
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)
anonymous
  • anonymous
Thank you, i just fanned u and gave you a medal and a testimonial
anonymous
  • anonymous
ive lerned more now than the past 2 months in algebra

Looking for something else?

Not the answer you are looking for? Search for more explanations.