Question

Реши два неравенства
98б

Answer 1

$1); ; |x^2-x+1|geq |x^2-3x+4|; ; to ; ; |x^2-3x+4|leq |x^2-x+1|\\star ; ; |A|<B; ; Rightarrow ; ; -B<A<B; ; star \\-(x^2-x+1)leq x^2-3x+4leq x^2-x+1; ; Rightarrow left { {{x^2-3x+4leq x^2-x+1} atop {x^2-3x+4geq -x^2+x-1}} right. \\a); ; x^2-3x+4leq x^2-x+1; ; ,; ; 3leq 2x; ,; ; xgeq frac{3}{2}\\b); ; x^2-3x+4geq -x^2+x-1; ,; ; 2x^2-4x+5geq 0; ,\\D/4=4-10=-6<0; ; Rightarrow ; ; 2x^2-4x+5>0; ; pri; ; xin (-infty ,+infty )\\Otvet:; xin [, frac{3}{2}, ,, +infty )$

$2); ; |x^2+x-6|<x\\-x<x^2+x-6<x; ; Rightarrow ; ; left { {{x^2+x-6<x} atop {x^2+x-6>-x}} right. ; left { {{x^2-6<0} atop {x^2+2x-6>0}} right. \\a); ; x^2-6<0; ,; ; (x-sqrt6)(x+sqrt6)<0; ,; sqrt6approx 2,4\\znaki:; ; +++(-sqrt6)---(sqrt6)+++quad xin (-sqrt6,+sqrt6)\\b); ; x^2+2x-6>0; ,; ; D/4=1+6=7; ,; x_{1,2}=-1pm sqrt7\\(x+1-sqrt7)(x+1+sqrt7)>0\\znaki:; ; ; +++(-1-sqrt7)---(-1+sqrt7)+++\\xin (-infty ,-1-sqrt7)cup (-1+sqrt7,+infty )$

$-1-sqrt7approx -3,6; ; ;; ; -1+sqrt7approx 1,6\\c); ; left { {{xin (-sqrt6,sqrt6)} atop {xin (-infty ,-1-sqrt7)cup (-1+sqrt7,+infty )}} right. ; ; Rightarrow ; ; xin (-1+sqrt7, ;, sqrt6)$