Question

dau coroana plus 100 puncte ​

Answer 1

$D(x) =\ \left|\begin{array}{ccc}x&x&x\\3&-1&x\\2&x&-1\end{array}\right|\\a)D(-2)=\ \left|\begin{array}{ccc}-2&-2&-2\\3&-1&-2\\2&-2&-1\end{array}\right|\\=-2*-1*-1+3*-2*-2+-2*-2*2-(2*-1*-2+3*-2*-1+-2*-2*-2)\\=-2+12+8-(4+6-8)\\=18-2=16\\\\b) D(x)=\ \left|\begin{array}{ccc}x&x&x\\3&-1&x\\2&x&-1\end{array}\right|\\=x+3x^2+2x^2+2x+3x-x^3\\=-x^3+5x^2+6x\\=x(-x^2+5x+6)\\=-x(x^2-5x-6)\\=-x(x-6)(x+1)\\=x(6-x)(x+1)$

c) de la punctul b) D(x)=x(6-x)(x+1), oricare x apartine lui R

=>$\\D(\sqrt{a} )=\sqrt{a} (6-\sqrt{a} )(\sqrt{a} +1)$

$(6\sqrt{a} -a)(\sqrt{a} +1)=0\\= > 6\sqrt{a} -a=0\\6\sqrt{a} =a\\a^2=36a\\a^2-36a=0\\a(a-36)=0\\a=0\\a=36\\\sqrt{a} +1=0\\\sqrt{a} =-1(a\ nu\ poate\ fi\ real)\\= > S={0,36}$