Question

Решить. вот этот пример x^3-3x^2-2x+6=0

Answer 1

X³-3x²-2x+6=0
x²(x-3)-2(x-3)=0
(x-3)(x²-2)=0
x-3=0⇒x=3
x²-2=0⇒x²=2⇒x=+-√2

Answer 2

F(x)=x^3-3x^2-2x+6=0
$F(3)=27-27-6+6=0 \\ F(x)=(x^3-3x^2)+(-2x+6)=x^{2}(x-3)-2(x-3) \\ F(x)=(x-3)(x^2-2) \\ a^2-b^2=(a-b)(+b) \\ F(x)=(x-3)(x- \sqrt{2})(x+ \sqrt{2}) \\ F(x)=0;x_{1}=- \sqrt{2};x_{2}= \sqrt{2};x_{3}=3$