Question

Se considera expresia E(x)=(x+3)²+2(x-4)(x+3)+(x-4)²,cu x€R .Aratati ca E(x) este patrat perfect si calculati a€R pentru care E(a) are cea mai mica valoare .

Answer 1

$E(x)= (x+3)^{2}+2(x-4)(x+3)+ (x-4)^{2}= [(x+3)+(x-4)]^{2} =$
$(2x-1)^{2}$
$E(a)=0=> (2a-1)^{2}=0=>a= \frac{1}{2}$