Question

E(x)=(2x-1)² +  2(2x-1)(x+1) + (x+1)²
a) Aratati ca E (x) se divivde cu 3 oricare ar fi ∈ R
b) Calculati media geometrica a numerelor a(√2 + √3 ) + b (√2 -√3) = √18 + √2

Answer 1

$a)E(x)=[(2x-1)+(x+1)]^2=(3x)^2=9x^2=\ \textgreater \ E(x)\vdots3$
[tex]b)a \sqrt{2} +a \sqrt{3} +b \sqrt{2} -b \sqrt{3} =3 \sqrt{2} + \sqrt{2} \\ \sqrt{2} (a+b-4)+ \sqrt{3}(a-b)=0\\ a+b-4=0=\ \textgreater \ a+b=4\\ a-b=0=\ \textgreater \ a=b=2\\ M_g= \sqrt{a\cdot b}= \sqrt{4} =2[/tex]