Find the range of $x$.

Question

mathmath333 · Answer

$\large \color{black}{\begin{align} (x+3)^2(x-5)>0\hspace{.33em}\~\
\end{align}}$

imqwerty · Answer

x>5

anonymous · Answer

@imqwerty could you explain how you got that?

idku · Answer

(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 · Answer

(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 · Answer

yes, we don't consider imaginaries....
these notations belong to R, and all that ... lol