Question

Help on Radical Equations!!

Answer 1

\[\sqrt{x-7+5}\]\[-4\sqrt{x+9} =20\] \[\sqrt{6x+5} \sqrt{53}\] \[\sqrt{x+2+4} =x\]

Answer 2

are these 4 different questions?

Answer 3

yes

Answer 4

What's so difficult in the first one?

Answer 5

I don't understand it? .. I'm not good at math, at all

Answer 6

what's -7 + 5?

Answer 7

-2

Answer 8

Right, so\[\sqrt{x -7 + 5} \to \sqrt{x-2} \to |x-2|\]

Answer 9

Oh, that makes sense

Answer 10

Sure it does.

Answer 11

..okay?..

Answer 12

Now, Solve the second one.

Answer 13

since the -4 is outside of the radical, how would I do that exactly?

Answer 14

Divide -4 from both sides.

Answer 15

-2.25 and -5

Answer 16

? (post #8) Khan, \[\sqrt{x-2}\rightarrow \left| x-2 \right| ?\]

Answer 17

@destinyshaw , now insert the values back in the equation if the solutions are real.

@CliffSedge , ummm.. yes.. Did i made a mistake? D:

Answer 18

I just don't see how the square root of (x-2) equals the absolute value of (x-2), or does that means something else?

Answer 19

Actually the main reason for the putting Modulus is that there can't be a negative number inside the radical. or else the result will not be real.

Answer 20

@CliffSedge ^
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Answer 21

that's fine, but if \[\sqrt{x-2} = \left| x-2 \right|\]
If you square both sides, \[\rightarrow x-2 = x^2-2x+4\]
I have to guess that you mean \[\sqrt{\left|x-s\right|}\] just to restrict the domain of the radicand, but I don't think that's necessary here, since it's just an expression to be simplified and not an equation.
BTW, so what if it's not a real number? ;-)

Answer 22

Sorry for interrupting and sidetracking you. :">

Answer 23

@CliffSedge , No no. it was good that you corrected me.
can you please tell me the difference again so i can understand it in a better way. Sorry but i didn't understood it. :/

Answer 24

Difference of what?
The first expression simplified to \[\sqrt{x-2}\] and that's really all that can be done with it. Since it isn't an equation, there's nothing to solve for, so there's no need to restrict the domain.
I understand taking the absolute value/modulus/magnitude to avoid imaginary numbers if your domain is restricted to real numbers, but it's easier just to say x>2.