mathmath333
  • mathmath333
solve for \(x\)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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mathmath333
  • mathmath333
\(\large \color{black}{\begin{align} (x-1)\sqrt{x^2-x-2}\geq 0\hspace{.33em}\\~\\ \end{align}}\)
mathmath333
  • mathmath333
i got \(\large \color{black}{\begin{align} x\geq 1 \cup \left(x\geq 2 \cup x\leq -1\right)\hspace{.33em}\\~\\ \end{align}}\)
freckles
  • freckles
\[x^2-x-2=(x-2)(x+1) \\ (x-1) \sqrt{(x-1)(x-2)} \ge 0\] we should consider the domain of the square root function there on that square root function's domain the square root function will be positive so then you just need to consider when (x-1) is positive and find the intersection of these sets

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mathmath333
  • mathmath333
how to solve this \(\large \color{black}{\begin{align} x\geq 1 \cup \left(x\geq 2 \cup x\leq -1\right)\hspace{.33em}\\~\\ \end{align}}\)
freckles
  • freckles
is that one symbol is suppose to be an intersect sign ?
mathmath333
  • mathmath333
i havent studied intersection of sets
mathmath333
  • mathmath333
i just tried and posted
freckles
  • freckles
we should also go back to include when the function is 0 but I think you mean \[(x \ge 1) \cap (x \ge 2 \cup x \le -1)\] draw a number line in keep in mind that x can be 1,-1,2 since that makes the function 0 but anyways it might helped to also graph that... |dw:1436976303765:dw|
freckles
  • freckles
notice the elements in common between x>=1 and also (x ge 2 union x<=-1)
freckles
  • freckles
|dw:1436976374511:dw|
freckles
  • freckles
|dw:1436976397456:dw| but we also want to include these little endpoints because at these endpoints we have the thingy is 0
freckles
  • freckles
the reason x<-1 doesn't work is because x-1 is negative there the reason 1
freckles
  • freckles
anyways intersect just means you are trying to find the common elements
mathmath333
  • mathmath333
u mean the answer is \(x\geq 2\)
mathmath333
  • mathmath333
but wolfram also gives \(x=-1\) which is not in ur intersecton
freckles
  • freckles
you need to include the zeros @mathmath333
freckles
  • freckles
x>=2 or x=1 or x=-1
freckles
  • freckles
this is what I meant by the statement "but we also want to include these little endpoints because at these endpoints we have the thingy is 0 "|dw:1436977880095:dw| and the drawing that went along with it
freckles
  • freckles
if the thing was just \[(x-1) \sqrt{(x+1)(x-2)} >0 \] the answer would have been to just look at the interesections
freckles
  • freckles
the intersection of when x>1 and the domain of the square root function
freckles
  • freckles
but we also had a equal sign in there
freckles
  • freckles
\[(x-1) \sqrt{(x+1)(x-2)} >0 \text{ gives the solution } x>2 \\ (x-1)\sqrt{(x+1)(x-2)}=0 \text{ when } x=\pm 1 \text{ or } x=2 \\ \]
freckles
  • freckles
therefore the solution to \[(x-1) \sqrt{(x+1)(x-2)} \ge 0 \text{ is } x>2 \text{ or } x= \pm 1 \text{ or } x=2 \\ \text{ clean it up a little } x \ge 2 \text{ or } x=\pm 1 \]

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