Question

aratati ca numarul n=(2x^2-3x+4)×(2x^2-3x+2)+1 este patrat perfect oricare ar fii numarul natural x.

Answer 1

[tex]m=(2x^2-3x+4)(2x^2-3x+2)+1,x\in~N \\ Fie~y\in~N~astfel~incat~y=2x^2-3x. \\ m=(y+4)(y+2)+1 \\ m=y^2+2y+4y+8+1 \\ m=y^2+6y+9 \\ \\ Deci~m=(y+3)^2 ~~~\checkmark [/tex]