anonymous
  • anonymous
(√x+10 ) + (√x-6) = 8 pls show work
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
Add like terms
anonymous
  • anonymous
2 sqrt[x]+10-6
anonymous
  • anonymous
2 sqrt[x]+4=8 2 sqrt[x]=4 (sqrt[x])^2=(2)^2 x=4

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yuki
  • yuki
littleice, is this the problem you need help with ?
anonymous
  • anonymous
i know the answer comes to 15
anonymous
  • anonymous
yes thanks
yuki
  • yuki
let me ask you something first is it \[\sqrt x +10\] or \[\sqrt{x+10}\]
anonymous
  • anonymous
\[\sqrt{x+10}+\sqrt{x-6}=8\]
yuki
  • yuki
okay, so our main goal is to get rid of the square roots. but before we proceed, there are things that you want to always remember about eqn.s that involves sqrt. it is that there are x's that are not allowed to use. since te number inside the radical has to be positive, first we have to note that x>-10 and x>6
anonymous
  • anonymous
i thought it was x cant equal -10 or 6?
yuki
  • yuki
if we get an answer that doesn't fall in this category, then there are no solutions. another thing that you have to do, (I'm not going to go into the detail unless you want to) is to check the answers when you get it. the gist of the reason has to do with the fact that\[x^2=k, means, x= \pm \sqrt{k}\]
yuki
  • yuki
-10 and 6 are actually ok. because sqrt(0) = 0 but sqrt(x) when x<0, becomes and imaginary number
anonymous
  • anonymous
k
yuki
  • yuki
alright let's proceed
yuki
  • yuki
when you get rid of sqrt.s you want to square them. but when you square both sides just as it is, you will end up having a square root again, so to avoid that, you will isolate one of the terms that has a square root around it, and deal with that first. as follows
yuki
  • yuki
\[(\sqrt{x+10})^2 = (8-\sqrt{x-6})^2\] so\[x+10 = 64 +16\sqrt{x-6}+(x-6)\]
yuki
  • yuki
now you only have one square root, so you isolate it and then square both sides again \[({x + 10 -64 -x +6 \over 16})^2 = \sqrt{x-6}^2\]
yuki
  • yuki
that way you will have a quadratic eqn. and you know how to solve it from there. don't forget to check the solutions, by plugging them in because sometimes they will fail.
yuki
  • yuki
\[(-3 )^2= \sqrt(x-6)^2\] is what you will get when you simplify the above so 9 = x -6 thus x =15
yuki
  • yuki
however, let's see what happens when we plug this back in into the original eqn. sqrt(15+10)+sqrt(15-6) =5+3 =8 which actually works. now we can guarantee that x =15.
yuki
  • yuki
did it help at all ?
anonymous
  • anonymous
idk what went thru my head but i got confused on how u did it did it a weird way and got the answer aswell
yuki
  • yuki
oh... ok :( let me know if you need any explanations though :)
anonymous
  • anonymous
heres how i did it \[\left( \sqrt{x+10} \right)^{2} = (8-\sqrt{x-6})^{2}\] \[x+10=64+16\sqrt{x-6} + \sqrt{x-6}\] \[x+10-64-x-6=16\sqrt{x-6}\] \[48^{2}=(16\sqrt{x-6})^{2}\] 2304=256x-6 2304/256=x-6 9=x-6 15=x
yuki
  • yuki
it is the same thing
yuki
  • yuki
I just divided 16 on both sides first

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