anonymous
  • anonymous
|x - 1| = |x2 -2x + 1|
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
|x-1|=|x-1|^2 therefore the real solution is x=1
anonymous
  • anonymous
You need to use the definition of absolute value and notice a couple of things. First,
anonymous
  • anonymous
\[|u|:=\sqrt{u^2}\]and so\[\sqrt{(x-1)^2}=\sqrt{(x^2-2x+1)^2}\]Square both sides and note you can factor the right-hand side as such:\[(x-1)^2=((x-1)^2)^2\]Hence,\[(x-1)^2=(x-1)^4 \rightarrow (x-1)^2(1-(x-1)^2)=0\]Therefore, either\[(x-1)^2=0 \rightarrow x=1\]or\[1-(x-1)^2=0 \rightarrow (x-1)^2=1 \rightarrow x-1=\pm 1 \rightarrow x=1 \pm 1\]That is,\[x=0,2\]

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anonymous
  • anonymous
So there are three solutions: x=0 x=1 x=2
anonymous
  • anonymous
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anonymous
  • anonymous
This is a plot of what you're trying to do. You have two functions,\[y=|x-1|\]and\[y=|x^2-2x+1|\]and you're trying to find the points of intersection.
anonymous
  • anonymous
THANK YOU SO SO MUCH LOKISAN AND IAMPAUL!
anonymous
  • anonymous
np :)
anonymous
  • anonymous
could you also help me with this , thanxs! |2x - 1| = x2
anonymous
  • anonymous
ok
anonymous
  • anonymous
I need a second to do something...
anonymous
  • anonymous
no problemo but i guess lokisan explains it miles better ;)
anonymous
  • anonymous
:)

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