anonymous
  • anonymous
help solve 1/2X=-1+sqrt(x-2)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
correction \[\frac{ 1 }{ 2 }x=-1 +\sqrt{x+2}\]
anonymous
  • anonymous
What you tried yet @Compgroupmail ?
anonymous
  • anonymous
I tried to bring it to the power by \[\frac{ 1 }{ 4 }x=1+(x+2)\] /is this correct?

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anonymous
  • anonymous
see (a+b)^2 is NOT equal to a^2 + b^2 only. \[\large{(\frac{1X}{2})^2 = (-1 + \sqrt{x-2})^2 }\] \[\large{\frac{x^2}{4} = 1 + x-2 - 2\sqrt{x-2} }\]
anonymous
  • anonymous
Oh wait in your corrected question it is x+2 not x-2 so it will be : \[\large{\frac{x} = 1+x-2 -2\sqrt{x+2}}\]
anonymous
  • anonymous
\[\large{\frac{x^2}{4} = 1+x-2 -2\sqrt{x+2}}\]
anonymous
  • anonymous
ok but I still don't understand how you broke it down to that. Can we go through it step by step?
anonymous
  • anonymous
Oh! Sorry I think I confused you, yes why not... so do you know the identity of (a+b)^2 = ?
anonymous
  • anonymous
a^2+2ab+b^2
anonymous
  • anonymous
Right! so in RHS (Right hand side) we have : -1 + sqrt{x+2} , correct?
anonymous
  • anonymous
left side of equation \[(\frac{ 1 }{ 2 }x)^2= \frac{ 1 }{ 4 }x\]. Correct?
anonymous
  • anonymous
right. That is the right hand side. What's next?
anonymous
  • anonymous
Yes , so square the right hand side ... that is : \[\large{( \sqrt{x+2} - 1 )^2 }\] Can you square that?
anonymous
  • anonymous
no. Not 100% how to do it. That's what's messing me up.
anonymous
  • anonymous
Wait for 1 minute, I am opening google chrome as IE is quite slow
anonymous
  • anonymous
ok no problem
anonymous
  • anonymous
add 1 to both sides and square both sides \[(\frac{ x }{ 2 } +1)^2 = x +2\]
anonymous
  • anonymous
\[ \frac{ x^2 }{4 } +x +1 = x+2\]
anonymous
  • anonymous
x^2 =4
anonymous
  • anonymous
ahh. I understand now :) THanks!

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