## anonymous 5 years ago sqrt x+2+sqrt x=4 lol i keep asking for help on this

1. anonymous

is that sqrt(x) + 2 or sqrt(x+2)

2. anonymous

well if its the former, x = 1 if the latter, x =49/16

3. anonymous

x=49/16 can you explain how you got this please?

4. anonymous

$\sqrt{x+2} + \sqrt{x} = 4$ $\iff \sqrt{x+2} = 4-\sqrt{x}$ Squaring both sides yields: $x+2 = 16 - 8\sqrt{x} + x \implies \sqrt x = \frac{7}{4}$ And squaring gives the result. Note, squaring can produce spurious roots, so we must check this back in the original equation, and see that it holds.

5. anonymous

16-8sqrt x+x can you explain that more

6. anonymous

(a-b)^2 = a^2 - 2ab + b^2 let a = 4 , b = sqrt(x)

7. anonymous

You're welcome. ¬_¬

8. anonymous

is this a formula (a-b)^2 = a^2 - 2ab + b^2

9. anonymous

Not a formula so much - well, it is an identity, but it's more just common sense of expanding brackets.

10. anonymous

um one more thing$\sqrt{x+2} +\sqrt{x-4}\rightarrow \sqrt{x+2}-4-\sqrt{x}$ how did the sqrt of x become negative when you move it

11. anonymous

Errr, what? That didn't happen, at all. Assuming your question was right, the 4 was never under the root... and was on the other side.

12. anonymous

i meant $\sqrt{x+2}+\sqrt{x} -4$

13. anonymous

Im still confused .......

14. anonymous

Im still confused .......