Odpowiedź:
4)
a) 49x² + 140x + 100 = 0
a= 49 , b = 140 , c = 100
∆ = b² - 4 * a * c
∆ = 140² - 4 * 49 * 100 = 19 600 - 19 600 = 0
x = -b/ 2a
x = - 140/ (2 * 49) = - 140/ 98 = - 1 3/7
b) x² + 6x + 9 = ( 2x - 1)²
x² + 6x + 9 = 4x² - 4x +1
x² + 6x + 9 - 4x² + 4x - 1 = 0
- 3x² + 10x + 8 = 0
a = - 3 , b = 10 , c = 8
∆ = b² - 4 * a * c
∆ = 10² - 4 * (-3) * 8 = 100 + 96 = 196
√∆ = √196 = 14
x1 = (-b - √∆)/2a
x1 = ( -10 - 14)/{2 *(- 3)} = -24/- 6 = 4
x2 = (-b+ √∆)/2a
x2 = ( -10+ 14)/{2*(-3)} = 4/-6 = - ⅔
c) 3x² +2x + 1 = 3x + 4x² - 3
3x² + 2x + 1 - 3x - 4x² + 3 = 0
- x² - x + 4 = 0
a= -1 , b = - 1, c = 4
∆ = b² - 4 * a *c
∆ = (-1)² - 4 * (-1) * 4 = 1 + 16 = 17
√∆ = √17
x1 = (-b -√∆)/2a
x1 = (1 -√17)/ -2
x2 = (-b +√∆)/2a
x2 = ( 1+√17)/ -2
d) 4 - ¼x² - 3x = x² + 2x + 9
4 - ¼x² - 3x - x² - 2x - 9 = 0
- 1 ¼x² - 5x - 5 = 0
- 5/4x² - 5x - 5 = 0. /*(- 4)
5x² + 20x + 20 = 0. /: 5
x² + 4x + 4 = 0
a = 1, b = 4 ,c = 4
∆ = b² - 4 * a * c
∆ = 4² - 4 * 1 *4 = 16 - 16 = 0
x = -b/2a
x = - 4/2 = - 2
Szczegółowe wyjaśnienie:
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