Question

sqrt(x-3)-sqrt(2x+1)=3

Answer 1

are you looking for x?

Answer 2

yes

Answer 3

square both sides
[swrt(x-3)]-[sqrt(2x+1)] = 3^2
Get
x-3-2x+1 = 9
(x-2x) + (-3+1) = 9
-x -2 = 9
Add 2
-x= 11
To get x by itself, and positive, divide by -1
x=-11

Answer 4

I tried replacing x with that value, it doesnt work

Answer 5

notice a couple errors...first of all always check your answers, if you plug in x=-11 you get sqrt of neg number thus it is not a solution

also, you didn't square left side properly...you have to FOIL

Answer 6

ORLY? okay, let me try again. I like that username, 'dumbcow' kudos to you.

Answer 7

OMGUSH. foil. FOIL. Shicuss me out of here, i suck

Answer 8

haha..yep the best username

Answer 9

okay, okay, so then help us out. what exactly are you foiling. the x-3 and 2x + 1?

Answer 10

\[[\sqrt{x-3} -\sqrt{2x+1}]^{2} = (x-3) -2 \sqrt{x-3}\sqrt{2x+1}+(2x+1)\]

Answer 11

AH. the same mistake i always make. Y'know, I made that same mistake on my math test two years ago.

Answer 12

common mistake with students...
\[(a-b)^{2} \ne a^{2} -b^{2}\]

Answer 13

dude, how do you get that fancy stuff? :I you're making me jelly. and hold on, I shall do this over again. FAILURE IS NOT AN OPTION.

Answer 14

@erick193 , are you still following? this is kinda a long problem with lot of steps

Answer 15

once you square both sides...next step is to isolate radical(s) on 1 side

Answer 16

Ahahhahaha. okay, jk, momma yelling at me right now, brb. if im not back, i hope you find the answer erick

Answer 17

and how you do that?

Answer 18

\[(x-3)-2\sqrt{x-3} \sqrt{2x+1}+(2x+1) = 9\]
(x-3) + (2x+1) = 3x-2 right?
\[-2\sqrt{x-3}\sqrt{2x+1} +3x-2 = 9\]
then move the 3x-2 to other side
\[-2\sqrt{x-3}\sqrt{2x+1} = 11-3x\]
divide by -2
\[\sqrt{x-3}\sqrt{2x+1} = \frac{11-3x}{-2}\]

Answer 19

so how do i get rid of radicals?

Answer 20

next step is square both sides again....always square both sides to get rid of radicals

this doesn't come out nice, are you sure the question is written correctly

Answer 21

yes

Answer 22

I just asked a classmate on FB and he says there is no solution

Answer 23

I also tried it and only keep getting radicals after I square

Answer 24

yes, there is no Solution....both answers are extraneous
but you still need to understand the steps so you can do other similar problems

when you square a radical , it goes away by definition
\[(\sqrt{x-3}\sqrt{2x+1})^{2} = (x-3)(2x+1)\]

Answer 25

ok..

Answer 26

the faster, easier way to check for No solution is graph it with calculator

http://www.wolframalpha.com/input/?i=sqrt%28x-3%29-sqrt%282x%2B1%29+%3D+3
notice the curve from left side never intersects with line y=3

Answer 27

So if the lines never intersect, it means no solution?

Answer 28

correct...solutions are points where 2 lines intersect

Answer 29

Is there a way to know if there is no solution without a graph calculator?

Answer 30

hmm well you could graph it by hand but like for this problem that would be too hard.

otherwise...you have to go through and solve for x, then plug them into original equation to see if they work, if None work then No solution

Answer 31

Ok thankyou!

Answer 32

your welcome