Question

(x^2+x+1)(x^2+x+2)-6=0

Answer 1

Ответ:

решение на фотографии

Answer 2

$(x^{2}+x+1)(x^{2}+x+2)-6=0\\\\x^{2}+x+1=m, \ \Rightarrow \ x^{2}+x+2=m+1\\\\m*(m+1)-6=0\\\\m^{2}+m-6=0\\\\m_{1}=-3\\\\m_{2}=2- \ teorema \ Vieta\\\\1)x^{2}+x+1=-3\\\\x^{2}+x+4=0\\\\D=1^{2}-4*4=1-16=-15<0-x\in\oslash\\\\2)x^{2}+x+1=2\\\\x^{2}+x-1=0\\\\D=1^{2}-4*(-1)=1+4=5\\\\x_{1}=\frac{-1-\sqrt{5} }{2}\\\\x_{2}=\frac{-1+\sqrt{5} }{2}$