## ganeshie8 Group Title i am getting two solutions for this problem. but only one is satisfying the equation. could someone pls explain whats going on... http://assets.openstudy.com/updates/attachments/50064e0ae4b0624180677e0a-emily9102-1342590484915-mathproblem5.jpg 2 years ago 2 years ago

1. f1r1e1s1h1 Group Title

square it and try?

2. ganeshie8 Group Title

|dw:1342591850277:dw|

3. ganeshie8 Group Title

x =1 is not satisfying the equation :( not sure why

4. ganeshie8 Group Title

hmm

5. f1r1e1s1h1 Group Title

man u have squared it so ofcourse one will not match?

6. higgs Group Title

when you square something, you will always get two solutions, and not all of them will be right. substitute the answers back into the original equation to check. in this case, 1 is not the solution as -1 is not equal to 1

7. ganeshie8 Group Title

im li'l lost.... could u elaborate pls.. ?

8. ganeshie8 Group Title

i see we are squaring... and losing sign sensitivity is it

9. mukushla Group Title

u must consider restrictions in every step note that when u have $$x-3=2 \sqrt{x}$$ then $$x-3 \ge0$$

10. ganeshie8 Group Title

ah that makes sense. thanks mukushla straight to the point. :)

11. mukushla Group Title

welcome my friend

12. higgs Group Title

I suppose this also applies to irrational equations like this? $\sqrt{x-1}+\sqrt{x+4}=\sqrt{3x+10}$ I got $$x = 5$$ and $$x = \frac{-13}{3}$$ $$x = \frac{-13}{3}$$ is rejected in this case as well because after substituting into the equation, it became undefined.

13. ganeshie8 Group Title

yeah now i understand thanks higgs :D here, from the first equation itself, we can apply the restriction x >=1. and hence rejected solutions < 1

14. No.name Group Title

The sollutions we get after solving , and which does not satisfy the origanal question are called extraneous sollutions. There occurred as we have squared , so there is a chance of getting a extraneous sollution.