## anonymous 5 years ago last problem, i swear *x+6*-*x-5*=1 The stars mean its in a radical

1. anonymous

$\sqrt{x+6}-\sqrt{x-5}=1$

2. anonymous

yes thats it

3. 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)

4. anonymous

how did you get that

5. 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.

6. anonymous

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

7. anonymous

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

8. anonymous

square both sides

9. anonymous

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

10. anonymous

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

11. anonymous

err

12. anonymous

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

13. anonymous

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

14. anonymous

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

15. anonymous

10 / 2 = sqrt (x-5)

16. anonymous

25 = x - 5 , x = 30

17. anonymous

THIS IS A JOKE

18. anonymous

anwar, we are trying to do the proof

19. anonymous

in my post

20. anonymous

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

21. 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$

22. anonymous

Sorry, third line should have a +7.

23. anonymous

how are you a champion?