Odpowiedź:
Zad. 3
a)
1/5x² + 5 = 2x
1/5x² - 2x + 5 = 0
∆= 4 - 4 = 0
x0 = 2 : 2/5 = 2 * 5/2 = 10 / 2 = 5
b)
2x² - 3✓2x = 4
2x² - 3✓2x - 4 = 0
∆ = 18 + 32 = 48
✓∆ = ✓48 = 4✓3
x1 = (3✓2 - 4✓3) : 4 = 3/4✓2 - ✓3
x2 = (3✓2 + 4✓3) : 4 = 3/4✓2 + ✓3
c)
3x² + 8x + 4 = 0
∆ = 64 - 48 = 16
✓∆ = 4
x1 = (-8 - 4) : 6 = -2
x2 = (-8 + 4) : 6 = -4/6 = -2/3
d)
5x = 4x² + 1
4x² - 5x + 1 = 0
∆ = 25 - 16 = 9
✓∆ = 3
x1 = (5 - 3) : 8 = 1/4
x2 = (5 + 3) : 8 = 1
e)
3x² + 2 = 7x
3x² - 7x + 2 = 0
∆ = 49 - 24 = 25
✓∆ = 5
x1 = (7 - 5) : 6 = 1/3
x2 = (7 + 5) : 6 = 2
f)
6x² = x + 1
-6x² + x + 1 = 0
∆ = 1 + 24 = 25
✓∆ = 5
x1 = (-1 - 5) : -12 = 1/2
x2 = (-1 + 5) : -12 = -1/3
Mogę naj?
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