Question

помогите плз  с примерами

Answer 1

$1.;log_{sqrt3}(-4x-x^2)-log_{sqrt[3]3}(-x)=2\O.D.3.:\begin{cases}-4x-x^2>0\-x>0end{cases}Rightarrowbegin{cases}x(4+x)<0\x<0end{cases}Rightarrow xin(-4;;0)\log_{sqrt3}(-4x-x^2)-log_{3^frac13}(-x)=2\log_{sqrt3}(-4x-x^2)-3log_{sqrt3}(-x)=2\log_{sqrt3}(-4x-x^2)-log_{sqrt3}(-x)^3=2\log_{sqrt3}frac{-4x-x^2}{-x^3}=2\frac{4+x}{x^2}=(sqrt3)^2\frac{4+x}{x^2}=3\3x^2-x-4=0$
$D=1+4cdot3cdot4=49\x_{1,2}=frac{1pm7}{6}\x_1=frac86=frac43=1frac13;-;HE;nogx.;no;O.D.3.\x_2=-1$
Ответ: x = -1
$2.;frac{x^2-8y^2}{x^frac23-2sqrt[3]{y^2}}-left(x^frac23+2sqrt[3]{y^2}right)^2=-2x^frac23y^frac23\frac{x^2-8y^2}{x^frac23-2sqrt[3]{y^2}}-left(x^frac23+2sqrt[3]{y^2}right)^2=frac{x^2-8y^2}{x^frac23-2{y^frac23}}-left(x^frac23+2y^frac23right)^2=\=frac{left(x^frac23-2y^frac23right)left(x^frac43+2x^frac23y^frac23+4y^frac43right)}{x^frac23-2{y^frac23}}-left(x^frac43+4x^frac23y^frac23+4y^frac43right)=$
$=x^frac43+2x^frac23y^frac43+4y^frac43-x^frac43-4x^frac23y^frac23-4y^frac43=-2x^frac23y^frac23$
ЧТД