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-x² + x = 0 1/3 x² + x = 0
-x (x - 1) = 0 x ( 1/3 x + 1) = 0
x = 0 lub x-1 =0 x = 0 lub 1/3 x + 1 = 0
x = 1 1/3 x = -1 /· 3
x = - 3
c) 1 - 6x = -9x² d) x² = 12x - 36
9x² -6x + 1 = 0 x² -12x +36 = 0
( 3x - 1 )² = 0 (x - 6) ² = 0
3x -1 = 0 x - 6 = 0
3x = 1 /:3 x = 6
x = 1/3
e) x(x+1) = 9x -16 f) (2-x) x = 4 - 2x
x² + x - 9x + 16 = 0 2x - x² -4 +2x = 0
x² - 8x + 16 = 0 -x² + 4x - 4 = 0 /·(-1)
(x - 4)² = 0 x² -4x + 4 = 0
x - 4 = 0 (x-2)² = 0
x = 4 x -2 = 0
x = 2
2) a) 54 x² - 6x = 0 /:6 b) 54x² + 6 = 0
9x² - x = 0 54x² = -6
x( 9x - 1) = 0 Równanie sprzeczne ,
x = 0 lub 9x-1 = 0 brak rozwiązania.
x = 1/9
Równanie ma 2 rozwiązania.
c) 54 x² - 6 = 0 /:6
9x² - 1 = 0
(3x-1) (3x+1) = 0
3x-1 = 0 lub 3x+1 = 0
3x = 1 3x = -1
x = 1/3 x = -1/3
Równanie ma 2 rozwiązania.