Question

Aratati ca este patrat perfect
$( x^{2} -x+2)( x^{2} -x+4)+1$

Answer 1

notam x²-x+2=a

a(a+2)+1= a²+2a+1=(a+1)²

refacem inlocuirea si obtinem (x²-x+2+1)²=(x²-x+3)²

Answer 2

(x²-x-2)(x²-x+4)+1=[(x+1)(x-2)](x²-x+4)+1=(x²-x-2)(x²-x+4)+1=
=x⁴-2x³-5x²+6x+9=(x²-x-3)²

x²-x-3=0
x²-x=3
x²-x+1/4=13/4
(x-1/2)²=13/4
x=1/2+√13/2
x=1/2-√13/2

Este patrat perfect!