Question

Помогите решить 1б, пожалуйста.
Срочно.

Answer 1

$x^{3}-25x=0; x( x^{2} -25)=0 \ left { {{x=0} atop { x^{2}-25 =0}} right. left { {{x=0} atop { x^{2} =25}} right. left { {{x=0} atop {x=+-5}} right.$
$frac{3y+2}{4 y^{2}+y } + frac{y-3}{16 y^{2}-1 }= frac{3}{4y-1} \ \ frac{3y+2}{y(4y+1)} + frac{y-3}{(4y-1)(4y+1)} - frac{3}{4y-1}=0 \ \ frac{(3y+2)(4y-1)+y(y-3)-3y(4y+1)}{y(4y-1)(4y+1)} =0 \ \ frac{ y^{2-y-2} }{y(4y-1)(4y+1)} =0 \ \ y^{2}-y-2=0, y neq 0,y neq +- frac{1}{4} \ \ D=1-4*1*(-2)=9 \ \ x_{1} = frac{1-3}{2}=-1; x_{2}= frac{1+3}{2}=2$
2.
$2 x^{2} -x-15 textgreater 0 \ \ D = 1 - 4*2*(-15)=121 \ \ x_{1} = frac{1-11}{4}=-2,5 ;x_{2}= frac{1+11}{4}=3$
x∈(-∞;2.5)∪(3;∞)
$x^{2} textless 16 \ x=+-4$
x∈(-∞;-4)∪(4;∞)
3.
$(x+11)(x+2)(x-9) textless 0$
x∈(-∞;-11)∪(-2;9)
$frac{x+3}{x-8} textgreater 0$
x∈(-∞;-3)∪(8;∞)
4.
$x^{4} -4 x^{2} -45=0 \ \ t= x^{2} \ \ t^{2} -4t -45 = 0\ \ D = 16 -4 *1(-45) = 196 \ \ t_{1} = frac{4-14}{2}= 5; t_{2}= frac{4+14}{2}=9 \ \ left { {{ x^{2} =5} atop { x^{2} =9}} right. left { {{x= sqrt{5} } atop {x=+-3}} right.$
5.
$2 x^{2} +nx + 8=0 \ \ n^{2}-4*2*8 textless 0 \ \ n^{2}- 64 textless 0 \ \ n^{2} textless 64 \ \ n textless 8$
n∈(-∞;8)
6.
$y= sqrt{3x-2 x^{2} } \ \ |3x-2 x^{2} | geq 0 \ \ left { {{3x-2 x^{2} geq 0} atop {2 x^{2} -3x geq 0}} right. \ \ 3x-2 x^{2} geq 0; x(3-2x) geq 0 \ \ left { {{x geq 0} atop {3-2x geq 0}} right. left { {{x geq =0} atop {x leq 1.5}} right. \ \ 2x^{2}-3xgeq 0 ;x(2x-3) geq 0\ \ left { {{x geq 0} atop {x geq 1.5}} right.$
x∈[-1.5;1.5]