Question

|х^2-11х-6|=6 полное решение плищ

Answer 1

Ответ:

$-1;\ 0;\ 11;\ 12$

Объяснение:

$\displaystyle |x^2-11x-6|=6\\\\1.\\\\x^2-11x-6=6\\\\x^2-11x-6-6=0\\\\x^{2} - 11 \; x - 12 =0\\\\ a=1 ,\ \ b=-11 ,\ \ c=-12\\\\ D = b^2 - 4ac = ( - 11)^2 - 4\cdot1\cdot( - 12) = 121 + 48 = 169\\\\\sqrt{D} =\sqrt{169} = 13\\\\ x_1=\frac{-b-\sqrt{D}}{2a}=\frac{11-13}{2\cdot1}=\frac{-2 }{2 }=-1\\\\ x_2=\frac{-b+\sqrt{D}}{2a}=\frac{11+13}{2\cdot1}=\frac{24}{2}=12$

$\displaystyle 2.\\\\x^2-11x-6=-6\\\\x^2-11x-6+6=0\\\\x^2-11x=0\\\\x(x-11)=0\\\\x=0\ \ \ \ \ \ \ \ \ \ x-11=0\\\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x=11$