Question

Rozwiaz nierownosc :

2(x-3) 1
______ <______
x(x-6) x-1


1 1 1
_____ +_____ > ______
x-2 x-1 x

Answer 1

(2(x-3))/(x(x-6))<1/(x-1)

(2(x-3)(x-1)-x(x-6))/(x(x-6))<0

 

(2(x-3)(x-1)-x(x-6))/

2(x-3)(x-1)-x(x-6)<0

2x^2-2x-6x+6-x^2+6x<0

X^2-2x+6<0

Delta=4-2*6=-8

Brak rozwiązań

1/((x-2))+1/((x-1))>1/x

(x(x-1)+(x-2)x-(x-2)(x-1))/(x(x-2)(x-1))<0

X^2-x+x^2-2x-x^2+x+2x-2<0

-x-2x+x+2x-2<0

 

X^2-2<0

X1=√2

X2=-√2

Rozwiazanie x∈<-√2;√2>