# Show that the statement " If $x$ is real number such that $x^3+4x=0$, then $x$ is 0." is true using direct method.
" If $x$ is real number such that $x^3+4x=0$, then $x$ is 0."
Let $p :$ If $x$ is real number such that $x^3+4x=0. and$q:x=0$. To show that the above statement is true using direct method, Let us assume that$p$is true. We have to show that$q$is true.$x$is a real number such that$x^3+4x=0\Rightarrow\:\:x(x^2+4)=0\Rightarrow\:$either$x=0$or$x^2+4=0$But$x^2+4$cannot be$0$since$x^2 \geq 0\:\: \forall x \in R\thereforex=0\therefore\$ The given statement is true.