mathmath333
  • mathmath333
Find the range of \(x\).
Mathematics
schrodinger
  • schrodinger
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mathmath333
  • mathmath333
\(\large \color{black}{\begin{align} (x+3)^2(x-5)>0\hspace{.33em}\\~\\ \end{align}}\)
imqwerty
  • imqwerty
x>5
anonymous
  • anonymous
@imqwerty could you explain how you got that?

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idku
  • idku
(x+3)^2 is always the component that is greater than 0. So x can't be equal to -3 (but we might not need this restriction yet). for this to be greater than zero x has to be greater than 5, because if x is not greater than 5, then you either get 0>0 or negative number>0
imqwerty
  • imqwerty
(x+3)^2 is always > 0 until and unless x=-3 but (x+3)^2 cannot = 0 so from here we get x belongs to (R-{3}) now we see (x-5). To satisfy the condition (x-5) should be >0 and therefore x>5 now we have to take a common rage out of the two ranges ---- x belongs to(R-{3}) and x>5 ..........so the common range that we get is x>5
idku
  • idku
yes, we don't consider imaginaries.... these notations belong to R, and all that ... lol

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