Question

(x+1)^1/2 +(2x-5)^1/2 = 3

Plz solve as fast as possible and reply soon. I have a test on Quadratics tommorow

Answer 1

@rajee_sam

Answer 2

@AravindG @Emily778 @Frostbite @grayp @help123please.

Answer 3

I'm not going to help you if your just gonna spam me. Sorry, but no thanks.

Answer 4

i would move one of the radicals to other side of equal sign
then square both sides

Answer 5

oh are you a spammer :{
haha yeah only ask once is best policy

Answer 6

my equations is not working

Answer 7

after squaring both sides
isolate remaining radical to one side
then square both sides again

@rajee_sam , try refreshing browser a couple times

Answer 8

you will then have a quadratic equation
set equal to 0
factor or use quadratic formula to solve

...
good luck try to follow those steps

Answer 9

sorry I missed the 6 in 2 of the steps

Answer 10

@rajee_sam I am not able to solve ahead, i have tried this question 20 times but i am not able to solve, kindly tell me each step, i have to solve 50 more of this type, so i will learn it if once you solve it completely

Answer 11

if all you want is the solution, there are other ways

http://www.wolframalpha.com/input/?i=sqrt%28x%2B1%29+%2Bsqrt%282x-5%29+%3D+3

it will even give you step-by-step if you register with the site

Answer 12

you see radicals in your equation.

If you see one radical keep it on one side of the equation and take everything else to the other side

eg. √ (x+ 1) - 3 = 15

keep the radical on the LHS and take the -3 to the RHS

Now you will have √ (x + 1) = 15 + 3 = 18

Now you square both sides and you can solve for x

But if you have two radicals like it is in our problem. Keep one radical on each side like I did.

And keep squaring and combining like terms until you are left with no radicals.

Now in our problem the last step I wrote was

(x + 3)² = 36 ( 2x -5) right??

Answer 13

yes, right....please progress...

Answer 14

now you have to expand the LHS and expand the RHS of the equation

you will have

x² + 6x + 9 = 72x - 180

now again combine like terms

x² - 66x - 171 = 0

now this is a quadratic equation which you can solve using quadratic formula.

You know quadratic formula right??

Answer 15

when you take -180 to the other side you will have to add +9 to +180, the solution is 3 and it isnt derived by this....

Answer 16

@rajee_sam

Answer 17

my bad yes

Answer 18

so it will be

x² - 66x + 189 = 0

Answer 19

yes i got the answer, thanks....but there is definately a shortcut method to do this whc is really helpful with regard to competitive exams...anyways basics always work the best...thank you!! @rajee_sam

Answer 20

( x - 63) ( x-3) will be your factors

So your solutions are x = 63 , 3

Now you have to check for extraneous solutions by substituting these values in your original equation. you will find only x = 3 satisfies the equation and 63 I an extraneous solution.

Answer 21

If you find the shortcut pl. teach me too

Answer 22

alright i got it! @rajee_sam thanks for answering it as a whole...i am sorry if i did not follow any ideal of "Openstudy" but i got it!! Definately if i get a shortcut, i will put it on this post itself with your tag....thanks again! have a good day/night....

Answer 23

i believe the shortcut is to say what 2 integers add up to 3
0+3
or
1+2

0+3 will not work
assuming 1+2
x+1 = 1 or 4

x+1 = 4 --> x=3
2(3) -5 = 1

sqrt4 + sqrt1 = 3
done

Answer 24

@dumbcow thanks man! that was good.....i have already given a medal but i would also give this post a medal anyway informally....thanks!

Answer 25

@rajee_sam hey @dumbcow has put a shortcut, its good we can use this approach...