Question

(х^2+3)^2=(х^2-3)(х^2+3)+6(х^2+3) докажите тождество

Answer 1

x^4+6x^2+9=(x^4 -9) +6x^2+18

x^4+6x^2+9=x^4-9+6x^2+18

x^4+6x^2+9=x^4+6x+9

чтд 

Answer 2

(x^2+3)^2=(x^2-3)(x^2+3)+6(x^2+3)
x^4+6*x^2+9-(x^2-3)*(x^2+3)-6*(x^2+3)=0

x^4+6*x^2+9-x^4+9-6*(x^2+3)=0

6x^2+18-6*(x^2+3)=0

6x^2+18-(6x^2+18)=0

6x^2+18-6x^2-18=0

18-18=0

0=0

Тождество доказано!