Question

last problem, i swear

*x+6*-*x-5*=1 The stars mean its in a radical

Answer 1

\[\sqrt{x+6}-\sqrt{x-5}=1\]

Answer 2

yes thats it

Answer 3

The answer is x = 30
(I knew 30+6 is 36 and the square root of that is 6 and 30-5 is 25 and the square root of that is 5 so 6-5 = 1)

Answer 4

how did you get that

Answer 5

I used guess and check on this one :P. but give me a moment and I may be able to figure out how to go through the steps to prove it.

Answer 6

Sigh. This one takes a little while to type out in LaTex :P Hold on..

Answer 7

sqrt ( x+6) = 1 + sqrt (x+5)

Answer 8

square both sides

Answer 9

x+6 = 1 + 2 sqrt (x+5) + (x+5)

Answer 10

x+6 - 1 - (x+5) = 2 sqrt (x+5)

Answer 11

err

Answer 12

sqrt ( x+6) = 1 + sqrt (x- 5)

Answer 13

x+6 = 1 + 2 sqrt ( x - 5) + x- 5 , when you square both sides

Answer 14

6 + 5-1 = 2 sqrt ( x - 5)

Answer 15

10 / 2 = sqrt (x-5)

Answer 16

25 = x - 5 ,
x = 30

Answer 17

THIS IS A JOKE

Answer 18

anwar, we are trying to do the proof

Answer 19

in my post

Answer 20

thanks for the help cantor, I was looking at conjugates for some reason

Answer 21

\[\sqrt{x+6} - \sqrt{x-5} = 1\] \[\sqrt{x-5} = \sqrt{x-6} - 1\]
squaring both sides \[x - 5 = x - 2\sqrt{x+6} - 7\]\[2\sqrt{x+6} = 12\]\[\implies x = 30\]

Answer 22

Sorry, third line should have a +7.

Answer 23

how are you a champion?