Question

Rozwiąż rownania

a) (x-2)(2x+5)=(x-2)²
b) (x+3)² <4
c)

Answer 1

A) (x - 2)(2x + 5) = (x - 2)^2
    (x - 2)(2x + 5) = x^2 - 4x + 4
    2x^2 - 5x - 4x - 10 = x^2 - 4x + 4
    2x^2 - 5x - 4x - 10 - x^2 + 4x - 4 = 0
    x^2 - 5x - 14 = 0
    delta = 25 + 56 = 81
    pierwiastek z delty = 9
    x1 = 5 + 9 / 2 = 14/2 = 7
    x2 = 5 - 9 / 2 = -4/2 = -2

b) (x + 3)^2 < 4
    x^2 + 6x + 9 < 4
    x^2 + 6x + 9 - 4 < 0
    x^2 + 6x + 5 < 0
    delta = 36 - 20 = 16
    pierwiastek z delty = 4
    x1 = -6 + 4 / 2 = -2/2 = -1
    x2 = -6 - 4 / 2 = -10/2 = -5