1.1++Classificació+nombres+reals.Equacions

Activitats amb equacions i el número i

1.-(a) Find all values of x which are roots of the equation x² + 5x + 6 = 0.

 (b) The roots of x² + 5x + 6 = 0 are each increased by 7. Find a quadratic equation that has these new numbers as roots.

2. (a) Solve the system of equations algebraically for (x, y): x + y = 42 x − y = 10  (b) Suppose that p is an even integer and that q is an odd integer. Explain why the system of equations x+y = p x−y = q has no positive integer solutions (x, y).

3.- Determine all pairs of positive integers (x, y) that satisfy the equation x 2 − y 2 = 420.

4.- Trobeu totes les solucions, les reals i les complexes, de les equacions següents: a) x³ −8 = 0 (b) x³ + 8 = 0 (c) x⁴ −1 = 0 (d) x² +6x+25 = 0

5.- Calcula el valor dels següents nombres imaginaris 1

<span style="background-color: transparent; color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 130%; text-decoration: none; vertical-align: baseline;"> Dona un criteri per calcular qualsevol potència de i.
 * <span style="background-color: transparent; color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 130%; text-decoration: none; vertical-align: baseline;">i² ||   || <span style="background-color: transparent; color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 130%; text-decoration: none; vertical-align: baseline;">i³  ||   || <span style="background-color: transparent; color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 130%; text-decoration: none; vertical-align: baseline;">i⁴  ||   || <span style="background-color: transparent; color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 130%; text-decoration: none; vertical-align: baseline;">i⁵  ||   || <span style="background-color: transparent; color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 130%; text-decoration: none; vertical-align: baseline;">i⁶  ||   ||
 * <span style="background-color: transparent; color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 130%; text-decoration: none; vertical-align: baseline;">i⁷ ||   || <span style="background-color: transparent; color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 130%; text-decoration: none; vertical-align: baseline;">i⁸  ||   || <span style="background-color: transparent; color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 130%; text-decoration: none; vertical-align: baseline;">i⁹  ||   || <span style="background-color: transparent; color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 130%; text-decoration: none; vertical-align: baseline;">i¹⁰  ||   || <span style="background-color: transparent; color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 130%; text-decoration: none; vertical-align: baseline;">i¹¹  ||   ||
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 130%;"><span style="background-color: transparent; color: #000000; text-decoration: none; vertical-align: baseline;">i 43 ||   || <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 130%;"><span style="background-color: transparent; color: #000000; text-decoration: none; vertical-align: baseline;">i 2520   ||   || <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 130%;"><span style="background-color: transparent; color: #000000; text-decoration: none; vertical-align: baseline;">i 121   ||   || <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 130%;"><span style="background-color: transparent; color: #000000; text-decoration: none; vertical-align: baseline;">i 843   || <span style="background-color: transparent; color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 130%; text-decoration: none; vertical-align: baseline;">i³  || <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 130%;"><span style="background-color: transparent; color: #000000; text-decoration: none; vertical-align: baseline;">i 727   ||   ||
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 130%;"><span style="background-color: transparent; color: #000000; text-decoration: none; vertical-align: baseline;">i 43 ||   || <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 130%;"><span style="background-color: transparent; color: #000000; text-decoration: none; vertical-align: baseline;">i 2520   ||   || <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 130%;"><span style="background-color: transparent; color: #000000; text-decoration: none; vertical-align: baseline;">i 121   ||   || <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 130%;"><span style="background-color: transparent; color: #000000; text-decoration: none; vertical-align: baseline;">i 843   || <span style="background-color: transparent; color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 130%; text-decoration: none; vertical-align: baseline;">i³  || <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 130%;"><span style="background-color: transparent; color: #000000; text-decoration: none; vertical-align: baseline;">i 727   ||   ||