De
oplossingen-
verzameling
van
(x² − 1)2 = (x² + x)2
is gelijk aan 		A.  { − 1, +1 }
B.  { − 1, +1, min1op2 }
C.  { − 1, min1op2 }
D.  { − 1, +1/2 }
E.  { + 1, +1/2 }
F.  { + 1, − 1, 1/2 }
A    B    C    D    E    F

[ 4-0505 - op net sinds 29.3.2020-(E)-30.10.2023 ]

Translation in   E N G L I S H

What is the
solution set of
(x² − 1)2 = (x² + x)2
 A.  
B.  
C.  
D.  
E.  
F.  

Oplossing - Solution

  (x² − 1) ² = (x² + x) ²
⇔ x² −1 = x² + x  ∨  x² −1 = −x² −x
⇔ x = −1  ∨  2x² + x − 1 = 0
⇔ x = −1  ∨  (x + 1)(2x − 1) = 0
⇔ x = −1  ∨  x = −1 ∨ x = 1/2
⇔ x = −1  ∨  x = 1/2
gricha