Question

Verificati egalitatea 1+(x²+x+3)(x²+x+1)=(x²+x+2)² , oricare ar fi numar real x

Answer 1

1+x⁴+x³+x²+x³+x²+x+3x²+3x+3=x⁴+x³+2x²+x³+x²+2x+2x²+2x+4
x⁴+2x³+5x²+4x+4=x⁴+2x³+5x²+4x+4

Answer 2

In primul termen notam x^2+x=y
1+(y+3)(y+1)=1+y^2+4y+3=
y^2+4y+4=(y+2)^2=
(x^2+x+2)^2
Unde notatia x^2 înseamnă x la puterea a doua