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2010-02-01T21:36:17+01:00
1 zadanie
a)x² - 2x=0
x( x -2) = 0
x = 0 lub x-2 = 0
x = 0 lub x = 2

b) 3x² + 8x = 0
x( 3x + 8) = 0
x = 0 lub 3x +8 = 0
x = 0 lub 3x = -8
x = 0 lub x = -8/3

c) 4x² - x/2 =0 /*2
8x² -x = 0
x( 8x -1) = 0
x = 0 lub 8x -1 = 0
x = 0 lub x = 1/8

d) x² = -7x
x² + 7x = 0
x( x +7) = 0
x = 0 lub x +7 = 0
x = 0 lub x = -7

2 zadanie
½x² = 9 /*2
x² = 18
x = ±√8
x = ±√4*√2
x = ±2√2

2x² - 1= 17
2x² = 17 +1
2x² = 18 /:2
x² = 9
x² -9 = 0
(x-3)(x+3) = 0
x -3 = 0 lub x+3 = 0
x = 3 lub x = -3

6x²- 1⅗ = 0
6x² - 8/5 = 0
2(3x² -4/5) = 0 /:2
3x² -4/5 = 0
x² = 4/5 :3
x² = 4/5*1/3
x² = 4/15
x= ±√(4/15)
x = (± √2 : √15)*(√15:√15)
x = ± √2*√15 :15
x = ± √30 : 15

1 - 2x² = 5+x²
-2x² -x² = 5 -1
-3x² = 4
x² = -4/3
nie ma takiej liczby , która podniesiona do kwadratu dawałaby liczbe ujemną


12 - 3x²=0
3(4 -x²) = 0 /:3
4 -x² = 0
(2 -x) (2 +x) = 0
2-x = 0 lub 2 +x = 0
x = 2 lub x = -2

6x² = 8-x²
6x² +x² =8
7x² =8
x² = 8/7
x = ±√(8/7
x = ± √8 : √7
x = ± √4*√2 : √7
x = ±( 2√2 :√7)*(√7 : √7)
x = ± 2√2*√7 :7
x = ±2√14 :7
x = ± 2/7*√14