anonymous
  • anonymous
last problem, i swear *x+6*-*x-5*=1 The stars mean its in a radical
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
\[\sqrt{x+6}-\sqrt{x-5}=1\]
anonymous
  • anonymous
yes thats it
anonymous
  • anonymous
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)

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anonymous
  • anonymous
how did you get that
anonymous
  • anonymous
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.
anonymous
  • anonymous
Sigh. This one takes a little while to type out in LaTex :P Hold on..
anonymous
  • anonymous
sqrt ( x+6) = 1 + sqrt (x+5)
anonymous
  • anonymous
square both sides
anonymous
  • anonymous
x+6 = 1 + 2 sqrt (x+5) + (x+5)
anonymous
  • anonymous
x+6 - 1 - (x+5) = 2 sqrt (x+5)
anonymous
  • anonymous
err
anonymous
  • anonymous
sqrt ( x+6) = 1 + sqrt (x- 5)
anonymous
  • anonymous
x+6 = 1 + 2 sqrt ( x - 5) + x- 5 , when you square both sides
anonymous
  • anonymous
6 + 5-1 = 2 sqrt ( x - 5)
anonymous
  • anonymous
10 / 2 = sqrt (x-5)
anonymous
  • anonymous
25 = x - 5 , x = 30
anonymous
  • anonymous
THIS IS A JOKE
anonymous
  • anonymous
anwar, we are trying to do the proof
anonymous
  • anonymous
in my post
anonymous
  • anonymous
thanks for the help cantor, I was looking at conjugates for some reason
anonymous
  • anonymous
\[\sqrt{x+6} - \sqrt{x-5} = 1\] \[\sqrt{x-5} = \sqrt{x-6} - 1\] squaring both sides \[x - 5 = x - 2\sqrt{x+6} - 7\]\[2\sqrt{x+6} = 12\]\[\implies x = 30\]
anonymous
  • anonymous
Sorry, third line should have a +7.
anonymous
  • anonymous
how are you a champion?

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