Formule van Cardano

Waar wordt in het dagelijks leven een derdegraadsvergelijking als x³+6x=8 voor gebruikt, oftewel wat heb je aan zo'n vergelijking?
En wat is precies de formule van Girolamo Cardano?

Imp
Leerling bovenbouw havo-vwo - woensdag 18 juli 2001

Antwoord

"Negative numbers have not been fully accepted until the 18th century. Gerolamo Cardano (1501-1576) who scorned them as numeri ficti, devoted two separate chapters in his Ars Magna, one to equations in the form x³ + mx = p and another to equations x³ = mx + p."

"Rule to solve x³+mx=n
Cube one-third the coefficient of x; add to it the square of one-half the constant of the equation; and take the square root of the whole. You will duplicate this, and to one of the two you add one-half the number you have already squared and from the other you subtract one-half the same... Then, subtracting the cube root of the first from the cube root of the second, the remainder which is left is the value of x
(Gerolamo Cardano, Ars Magna, 1545)."

Meer weten?

• Quadratic, cubic and quartic equations
• The Development of Algebra in the Renaissance
  
• Girolamo Cardano

woensdag 18 juli 2001

Re: Formule van Cardano

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