Question

If x = 2+square root of 3 divided by 2-square root of 3, find: x-1 over x

Answer 1

For messy problems like this, I like to substitute \[a = \sqrt{3}\]do the algebra, then substitute back at the end, after the dust has settled. Your mileage may vary.

Answer 2

\[x=(2+\sqrt{3})/(2-\sqrt{3})\]
multiply conjugate -> 2+sqrt(3) to top and bottom
\[=(2+4\sqrt{3}+3)\]
plugin for x-1/x

\[((2+4\sqrt{3}+3)-1)/(2+4\sqrt{3}+3) =( 4+4\sqrt{3})/(5+4\sqrt{3})\]
multiply conjugate again -> 5-4sqrt(3) to top and bottom

= \[(4\sqrt{3}-28)/53\]
= aprox. -0.398

Answer 3

the answer is 8 multiply square root of 3

Answer 4

Well, can't shoot a guy for trying. It's been a while

Answer 5

thanks for trying

Answer 6

simplifying, you should get \(\large x=7+4\sqrt3 \)

Answer 7

now plug that in for (x-1)/x

Answer 8

and simplify again....

Answer 9

\[x=\frac{ (2+\sqrt{3})}{(2-\sqrt{3}) } \times \frac{ (2+\sqrt{3}) }{(2+\sqrt{3}) } = \]
You'll get what @dpaInc posted.

Answer 10

right i know that part but then i was stuck on the second part. i didnt know i had to plug it

Answer 11

\[\frac{ x -1 }{ x } =\frac{ 7+4\sqrt3-1 }{ 7+4\sqrt3 } \times \frac{ 7-4\sqrt3 }{ 7-4\sqrt3 }\]

Answer 12

^ again, I multiplied by the conjugate of the denominator
\[\frac{ 6+4\sqrt3 }{ 7+4\sqrt3 } \times \frac{ 7-4\sqrt3 }{ 7-4\sqrt3 } = \frac{ 42+28\sqrt3-24\sqrt3-16*3 }{49-16*3 }\]

Answer 13

i have the answer as 8 multiplied by square root of 3

Answer 14

hmm... maybe I've made a mistake.

Answer 15

Nope, my answer is correct.

Answer 16

i have the answer in my textbook as 8 multiplied by square root of 3

Answer 17

Are you sure you wrote the problem correctly? is it

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

Answer 18

Check it on a calculator. x = 13.928

Then find\[\frac{ x-1 }{ x }\] and you'll get 0.928.

Then check \[8\sqrt3 = \] and you'll get 13.856.

Answer 19

ill check it just give me a sec

Answer 20

they are almost the same. im wondering where 8 multiplied by square root of 3 came from

Answer 21

They aren't almost the same. x is close to 8sqrt3... but (x-1)/x is not even close to 8sqrt3.

Answer 22

i believe this problem can only be solved by a calculator as it is a digital worksheet. sorry made a mistake