# How to solve this type of sum using indirect proof. For any real number x, if x^3+2x+33!=0, then x+3!=0

How to solve this type of sum using indirect proof. For any real number $x$ , if ${x}^{3}+2x+33\ne 0$ , then $x+3\ne 0$
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Proving by contrapositive: Let $P$ be the statement ${x}^{3}+2x+33\ne 0$, $Q$ be $x+3\ne 0$. We wish to show that ¬Q⟹¬P$\mathrm{¬}Q\phantom{\rule{thickmathspace}{0ex}}⟹\phantom{\rule{thickmathspace}{0ex}}\mathrm{¬}P$.
If $\mathrm{¬}Q$, then $x+3=0$ and $x=-3$. Hence ${x}^{3}+2x+33=\left(-3{\right)}^{3}+2\left(-3\right)+33=0$, and we establish $\mathrm{¬}P$.