## anonymous 5 years ago help how do u solve sqrt(x)+sqrt(2x)=1

1. anonymous

3-2sqrt(2)

2. anonymous

is it possible to explain or show me how you got this

3. anonymous

yes, first square both sides

4. anonymous

add them together you get (3+2sqrt(2))x=1

5. anonymous

this is tricky, you realize that if you multiply by the complement, you get 9-8 which equals 1

6. anonymous

oh ok i understand it now i know ho to do the ones with one sqrt but wasnt sure how to do it with two sqrt's thanks

7. anonymous

sometimes it takes just a little flash of insight

8. anonymous

wait i just got lost were did you get the 3 from

$(\sqrt{x}+\sqrt{2x})^{2}$

that should result in: 3x plusminus (2x)2^1/2. But he omitted squaring the other side getting a 1

and the equating that ugly thing to 1 and solving, so far I haven't seen a solution.

12. anonymous

well the solution is 3-2$\sqrt{2}$

13. anonymous

i mean t 3-2sqrt(2)

14. anonymous

but i dont know how he got that i got lost after i looked back again

15. anonymous

see, the thing is (3+2sqrt(2))(3-2sqrt(2))=(3)^2-(2sqrt(2))^2

16. anonymous

which is 9-8=1

17. anonymous

the COMPLEMENT of (3+2sqrt(2)) is (3-2sqrt(2)) b/c that is like squaring both elements.

So your using + root, a - root. Is that a fair statement?