Question

помогите пожалуйста

Answer 1

$frac{x^3-x^2-x+1}{x+1} + frac{4}{x^2-2x+1} leq 5\\ frac{x^2(x-1)-(x-1)}{x+1} + frac{4}{(x-1)^2} leq 5\\ frac{(x-1)(x^2-1)}{x+1} +frac{4}{(x-1)^2} leq 5\\ frac{(x-1)(x-1)(x+1)}{x+1} + frac{4}{(x-1)^2} -5 leq 0\\(x-1)^2+frac{4}{(x-1)^2}-5 leq 0\\t=(x-1)^2; ,; ; frac{t^2-5t+4}{t} leq 0; ,; ; frac{(t-1)(t-4)}{t} leq 0\\Znaki:; ; ---(0)+++(1)---(4)+++$

$tin (-infty ,0)cup [, 1,4, ]; ; to$

 $left { {{(x-1)^2 textless 0; net; reshenij} atop {1<=(x-1)^2<=4}} right.$ 

$left { {{(x-1)^2 geq 1} atop {(x-1)^2 leq 4}} right. ; left { {{(x-1)^2-1 geq 0} atop {(x-1)^2-4 leq 0}} right. ; left { {{(x-1-1)(x-1+1) geq 0} atop {(x-1-2)(x-1+2) leq 0}} right. ; left { {{(x-2)x geq 0} atop {(x-3)(x+1) leq 0}} right. \\ left { {{x leq 0; ili; x geq 2} atop {-1 leq x leq 3}} right. ; ; Rightarrow ; ; xin [-1;0, ]cup [, 2;3, ]\\ODZ:; ; xne -1; ;; xne 1\\Otvet:; ; (-1;0, ]cup [, 2;3, ]$

$2); ; frac{sqrt2cosx-1}{sqrt{-5sinx}} =0; ; to ; ; left { {{sqrt2cosx-1=0} atop {sinx textless 0}} right. \\ left { {{cosx=frac{1}{sqrt2}=frac{sqrt2}{2}} atop {-pi +2pi n textless x textless 2pi n,; nin Z}} right. ; ; left { {{x=pm frac{pi}{4}+2pi k,; kin Z} atop {-pi +2pi n textless x textless 2pi n,; nin Z}} right. \\x=-frac{pi}{4}+2pi n,; nin Z\\xin [, frac{3pi }{2};3pi , ]; ; to ; ; ; x=frac{7pi}{4}$