Show that the statement .
p : 'If x is a real number such that `x^(3)+ 4x=0,` then x=0' is true by
Method of contradiction

Answer

Method of contradiction :
Let x ≠ 0, and let x=p,p `in` R and p is a root of `x^(3)+4x=0=>p^(3)+4p=0=>p(p^(2)+4)=0.` but p ≠ 0 (assumption),also `p^(2)+4 ≠ 0=> p(p^(2)+4),i.e., p^(3)+4p ≠ 0` This contradicts the given statement. So our assurnption that x ≠ 0 is wrong Hence, x =0.