Question

e^-1/2 x ((1+2x)^-1/2 - 1/2(1+2x)^1/2) = 0 find x

Answer 1

\[\large e^{-\frac{1}{2}x} (1+2x)^{-\frac{1}{2}} - \frac{1}{2}(1+2x)^{\frac{1}{2}} = 0\]

Answer 2

Is this right?

Answer 3

i ve edited the ques. sorry my mistake.

Answer 4

\[\large e^{-\frac{1}{2}x} ( (1+2x)^{-\frac{1}{2}} - \frac{1}{2}(1+2x)^{\frac{1}{2}}) = 0\]

Is this good now?

Answer 5

yeag

Answer 6

See:
\[\large a^{-x} = \frac{1}{(a)^x}\]

Answer 7

i know how to solve but i couldnt get the answer. could you pls write out the steps for me to get x. thanks.

Answer 8

So:
\[(1 + 2x)^{-\frac{1}{2}} = \frac{1}{(1+2x)^{\frac{1}{2}}}\]

Answer 9

What answer you got? Tell me that first and allow me to find where you have done mistake(s)..

Answer 10

x=1/2?

Answer 11

\[\frac{e^{-x/2}}{(1+2x)^{1/2}}[1 - (1+2x)] = 0 \\ 1 - 1 - 2x = 0 \implies x = 0\]

Answer 12

what? x=0?

Answer 13

Nope..

Answer 14

I missed 1/2 in front..

Answer 15

huh?

Answer 16

\[\frac{e^{-x/2}}{(1+2x)^{1/2}}[1 - \frac{1}{2}(1+2x)] = 0 \\ 1 - \frac{1}{2} - x = 0 \implies x = \frac{1}{2}\]

Answer 17

You are right, why you think you are wrong?

Answer 18

wait. cant we just solve from ((1+2x)^−1/2−1/2(1+2x)^1/2)=0

Answer 19

Boxes everywhere..

Answer 20

huh?

Answer 21

refresh it.

Answer 22

I am not able to see what you wrote there, I am seeing boxes.

Answer 23

Yes you can.. You will get the same..

Answer 24

how?

Answer 25

show me the working maybe?

Answer 26

Just do what I did..

Answer 27

no. what if i wanna do it that way, the one i ask

Answer 28

\[\frac{1}{(1+2x)^{1/2}} - \frac{1}{2}(1+2x)^{1/2} = 0 \\ \frac{1}{(1+2x)^{1/2}}[1 - \frac{1}{2}(1+2x)] = 0\]

Answer 29

Now, put the other term to \(0\), and find \(x\) from there..

Answer 30

nooo. i mean from (1+2x)^-1/2 = 1/2 (1+2x)^1/2

Answer 31

how do you solve this.

Answer 32

Okay..

Answer 33

\[\frac{1}{(1+2x)^{1/2}} = \frac{1}{2}(1+2x)^{1/2} \]

Answer 34

uh huh

Answer 35

Square both the sides, instead of doing "huh", just try to understand what I did..

Answer 36

i was acknowledging to what you did there.

Answer 37

Don't square both sides..

Answer 38

i'm not getting what you trying to say. Youre confusing me

Answer 39

Multiply by (1+2x)^(1/2) both sides:
\[1 = \frac{1}{2}(1+2x) \\ 1 + 2x = 2 \\ 2x = 1 \implies x= \frac{1}{2}\]

Answer 40

how about 1/2 = (1+2x)^-1/2 / (1+2x) ^1/2

Answer 41

You can do it in thousand number of ways, I have provided you with enough steps that you can utilize them to understand it..

Answer 42

no im trying to try out a few steps. thats the only step i got in my mind.

Answer 43

if you're reluctant to enlighten me please do say so.

Answer 44

Use the very first formula I gave..

Answer 45

\[(1+2x)^{-1/2} = ??\]

Answer 46

isn't in 1 instead of x on the rhs?

Answer 47

What? Come again..

Answer 48

1/2 = (1+2x)^-1/2 / (1+2x) ^1/2 this. after solving isn't it 1 instead of x

Answer 49

Where?
Solve it and show..

Answer 50

(1+2x)^1/2 / (1+2x)^1/2 = 1 no?

Answer 51

No..

Answer 52

x?

Answer 53

\[\frac{1}{2} = \frac{(1+2x)^{-1/2}}{(1+2x)^{1/2}}\]

Answer 54

Don't do anything else now..
Use that formula which I gave..

Answer 55

\[(1+2x)^{-1/2} = ??\]

Answer 56

nevermind lol thanks. youre still not answering my ques. and you insist of using your way.

Answer 57

nevermind, your question is still not clear to me. Ask it in a good way otherwise show it if I am not getting it..

Answer 58

And I am stressing my way as I am not getting your way.. :P