Question

aratati ca expresia
E(x)= $\frac{(3x+1)^{2}+ (x-3)^{2} }{(2x-1)^{2} + (x+2)^{2} }$ , este un numar natural ∨∈R

Answer 1

$E(x) = \frac{(2x+1)^2+(x-3)^2}{(2x-1)^2+(x+2)^2} = \frac{9x^2+6x+1+x^2-6x+9}{4x^2-4x+1+x^2+4x+4} = \frac{10x^2+10}{5x^2+5} = \frac{2(5x^2+5)}{5x^2+5} =2$