Wat is de
oplossingenverzameling
van   x < x2 < x3   ? 		A.   ∅
B.   rplus
C.   r
D.   r \ [ 0, 1 ]
E.   ] 1, plusoneindig [
Rplus = { x | x ≥ 0 } rplusnul = { x | x > 0 } 
A    B    C    D    E

[ 5-1416 - op net sinds 13.4.15-(E)-26.7.2024 ]

Translation in   E N G L I S H

What is the
solution set
of
  x < x2 < x3   ? 		A.   ∅ none
B.   Rplus x ≥ 0
C.   R all x
D.   R \ [ 0, 1 ] x <0 ; x > 0
E.   ] 1, ∞ [ x > 1

Oplossing - Solution

          x < x² < x³
        x < x ²     ∧     x² < x³
    x − x² < 0   ∧   x² − x³ < 0
    x(1 − x) < 0   ∧   x²(1 − x)
     0 1     0   1
 x  |  0    1   .       x   |     0     1   .
x(1−x) |  − 0   +   0   −     x²(1−x)|   +   0   +   0   −
Op beide schema's zien we dat enkel voor getallen groter dan 1 de beide producten negatief zijn
GWB