De oplossingenverzameling
van de bikwadratische
vergelijking
16x4 = 49x2 − 3

bestaat uit
A.   2 rationale getallen
B.   2 rationale en 2 irrationale getallen
C.   2 irrationale getallen
D.   2 rationale en 1 irrationaal getal
E.   2 irrationale en 1 rationaal getal
A    B    C    D    E 

[ 5-4170 - op net sinds 15.12.06-(E)-20.7.2024 ]

Translation in   E N G L I S H

The set of solutions of
the biquadratic equation
16x4 = 49x2 − 3
consists of
A.   2 rational numbers
B.   2 rational numbers and 2 irrational numbers
C.   2 irrational numbers
D.   2 rational numbers and 1 irrational number
E.   2 irrational numbers and 1 rational number

Oplossing - Solution

16x4 = 49x2 − 3
⇔ 16x⁴ − 49x² + 3 = 0
⇔ 16y² − 49y + 3 = 0  ∧  y = x²
⇔ (y − 3)(16y − 1) = 0  ∧  y = x²
[y = 3  ∨  y = 1/16 ]  ∧  y = x²
⇔ x² = 3  ∨  x² = 1/16
⇔ x = ±1op3  ∨  x = ± 1/4
twee irrationale en twee rationale getallen
gricha