Matematicas 4 Nivel

Matemáticas cuarto nivel

2.- 3-5/(x-1)≥5/x 3/1-5/(x-1)-5/x≥0

(3(x^2-x)-5x-5x+5)/((x-1)(x))≥0

(3x^2-3x-5x-5x+5)/((x-1)(x))

(3x^2-13x+5)/(x-1)(x) ≥0

(3x^2-13x+5)

(x-1)(x-10/3)=0

x=(-b±√(b^2-4ac))/2a

x=(13±√(169-4(3)5))/6

x=(13±√(169-120))/6

x=(13±√49)/6

x=(13+7)/6=20/6=10/3

x=(13-7)/6=6/6=1

1.- (-1)≥0 ∧ (x-10/3)≥0 ∧ (x-1)>0 ∧ x>0

x≥1 ∧ x≥10/3 ∧ x>1 ∧ 1x>0

[10/3 ;∞^+ ┤[

0 1 10/3

2.- x-1≥0 ∧ (x-10/3)≥0 ∧ (x-1)<0 ∧ x<0

x≥1 ∧ (x-10/3)≥0 ∧ (x-1)<0 ∧ x<0

0 1 10/3

3.- (x-1)≥0 ∧ (x-10/3)≤0 ∧ x-1>0 ∧ x<0

x≥1 ∧ x≤10/(3 ) ∧ x>1 ∧ x<0

0 1 10/3 ∅

4.- (x-1)≥0 ∧ x-10/3 ≤0 ∧ x-1<0 ∧ x>0

x≥1 ∧ x≤10/(3 ) ∧ x<1 ∧ x>0

∅

0 1 10/3

A*ba*b≫0 (x+2)(x-3)≥0

a.- + ∧ + - ∧ -

x+2≥0 ∧ x-3≥0

b.- - ∧ -

x+2≥0 ∧ x-3≤0

x≤-2 ∧ x≤3

-2 0 3

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