## mathmath333 one year ago Find the range of $$x$$.

1. mathmath333

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

2. imqwerty

x>5

3. anonymous

@imqwerty could you explain how you got that?

4. 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

5. 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

6. idku

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