Question

Rozwiąż równanie :

a) x kwadrat + 9 = 6x
b) 4 x kwadrat + 9 = 12 x
c) 16 x kwadrat = 1
d) 25 x kwadrat = 9
e) 2 x kwadrat = 1
f) 9 x kwadrat = 6

Answer 1

A)
x² + 9 = 6x
x² - 6x + 9 = 0
(x - 3)² = 0
x - 3 = 0
x = 3

b)
4x² + 9 = 12x
4x² - 12x + 9 = 0
(2x - 3)² = 0
2x - 3 = 0
2x = 3 /:2
x = 3/2
x = 1,5

c)
16x² = 1
16x² - 1 = 0
(4x + 1)(4x - 1) = 0
4x + 1 = 0                           4x - 1 = 0
4x = -1/:4                            4x = 1/:4
x = -1/4                                 x = 1/4

d)
25x² = 9
25x² - 9 = 0
(5x + 3)(5x - 3) = 0
5x + 3 = 0                   5x - 3 = 0
5x = -3/:5                    5x = 3 /:5
x = -3/5                         x = 3/5

e)
2x² = 1/:2
x² = 1/2 /√
x = √1/2                          x = -√1/2

f)
9x² = 6 /:9
x² = 6/9
x² = 2/3 /√
x = √2/3                        x = -√2/3