Question

Se consideră expresia E(x) = (-x+x²)²+4x³, unde x este număr real.
a) Arată că E(-1) = E(0)

Answer 1

Răspuns:

$\boxed{E(x)=(-x+x^{2} )^{2} +4x^{3}}\\ \\E(-1)=[-(-1)+(-1)^{2} ]^{2} +4\times(-1)^{3} \\E(-1)=(1+1)^{2} +4\times(-1)\\E(-1)=2^{2} -4\\E(-1)=4-4\\\bf\purple{E(-1)=0}\\\\E(0)=(-0+0^{2} )^{2} +4\times0^{3}\\ E(0)=(-0+0)+0\\\bf\green{E(0)=0}$

⇒$\bf\purple{E(-1)} = \bf\green{E(0)}$