Question

De rezolvat acest exercitiu.

Answer 1

 

$\displaystyle\\a)\\D=\left|\begin{array}{ccc}a&b&c\\c&a&b\\b&c&a\end{array}\right|\\\\D=a^3+b^3+c^3-abc-abc-abc\\\\D=a^3+b^3+c^3-3abc\\\\a=-1;~b=2;~c=- 3\\\\D=(-1)^3+2^3+(-3)^3-3\timex (-1)\times2\times(-3)\\\\D=-1+8-27-18\\\\\boxed{\bf D=-38}$

$\displaystyle\\b)\\\\\left|\begin{array}{ccc}x&1&1\\1&x&1\\1&1&x\end{array}\right|=0\\\\\\x^3+1+1-x-x-x=0\\\\x^3-3x+2=0\\~~~~~~~~~~~0x^2=2x^2-2x^2\\~~~~~~~~~~~-3x=-4x+x\\\\x^3+2x^2-2x^2-4x+x+2=0\\\\(x^3+2x^2)+(-2x^2-4x)+(x+2)=0\\\\x^2(x+2)-2x(x+2)+(x+2)=0\\\\(x+2)(x^2-2x+1)=0\\\\(x+2)(x-1)^2=0\\\\(x+2)(x-1)(x-1)=0\\\\\boxed{\bf x_1=-2;~~x_2=1;~~x_3=1}$