Question

Rezolva ecuatia (x^2+x+1)(x^2+x+2)=12

Answer 1

 (x^2+x+1)(x^2+x+2)=12
x^4+x³+2x²+x³+x²+2x+x²+x+2=12
x^4+2x³+4x²+3x+2=12
x^4+2x³+4x²+3x+2-12=0
x^4-x³+3x³-3x²+7x²+10x-10=0
x³(x-1)+3x²(x-1)+7x(x-1)+10(x-1)=0
(x-1)(x³+3x²+7x+10)=0
(x-1)(x³+2x²+x²+2x+5x+10)=0
(x-1)(x²(x+2)+x(x+2)+5(x+2))=0
(x-1)(x+2)(x²+x+5)=0
x-1=0
x+2=2
x²+x+5=0
x=1
x=-2
x nu apartine R
deci x ∈ (-2,1)