yrivers36
  • yrivers36
Solve each equation symbolically. With explanation please. sqrt (x)+1=sqrt (x+2)
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
hint... \[\LARGE \sqrt x+1=\sqrt{x+2}\] square both sides..
yrivers36
  • yrivers36
Im not sure but I think I should foil left side of problem
yrivers36
  • yrivers36
\[(\sqrt{x}+1)(\sqrt{x}+1)-x+2\]

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yrivers36
  • yrivers36
thats an = in front of x
anonymous
  • anonymous
\[\LARGE (\sqrt x+1)^2=(\sqrt{x+2})^2\] \[\LARGE (\sqrt x)^2+2\cdot \sqrt{x}\cdot 1+1^2=x+2\] \[\LARGE x+2\cdot \sqrt{x}=x+2-1\] \[\LARGE 2\cdot \sqrt{x}=x-x +2-1\] \[\LARGE 2\cdot \sqrt{x}=1\] \[\LARGE \sqrt{x}=\frac12\] square both sides and there you go :)
anonymous
  • anonymous
can you do it ?
yrivers36
  • yrivers36
solution manuel says x = 1/4
anonymous
  • anonymous
that's correct. Well done ! ;)
yrivers36
  • yrivers36
Thank you once again :)
anonymous
  • anonymous
Glad to help :)

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