Question

Arata ca 4x la a patra + 1 = [x patrat + (x+1) la patrat ] [x patrat + (x-1) la patrat]
Help :3

Answer 1

[tex]4x^4+1=(2x^2)^2+1^2=(2x^2)^2+2\cdot 2x^2\cdot 1+1-2\cdot 2x^2\cdot 1=\\ =(2x^2+1)^2-(2x)^2=\\ =(2x^2+1-2x)(2x^2+1+2x)=\\ =[x^2+(x-1)^2][x^2+(x+1)^2][/tex]