Question

x patrat -x + 1 totul la patrat =?

Answer 1

$\ Folosim formula:\\ \\ (a+b+c)^2 = a^2+b^2+c^2 + 2(ab+ac+bc) \\ \\ \\ (x^2-x+1)^2 = (x^2)^{^2}-x^2+1 + 2\cdot [x^2\cdot(- x) + x^2\cdot 1 + (-x)\cdot 1] \\ \\ \Rightarrow (x^2-x+1)^2 = x^4 - x^2+1+ 2\cdot (-x^3+x^2-x) \Rightarrow \\ \\ \Rightarrow (x^2-x+1)^2 = x^4-x^2+1-2x^3+2x^2-2x \RIghtarrow \\ \\ \Rightarrow (x^2-x+1)^2 = x^4-2x^3+x^2-2x+1$