b) 0,5x² - x + 8 = 0
a = 0,5
b = -1
c = 8
Δ = b² - 4ac
Δ = (-1)² - 4•0,5•8 = 1 - 16 = -15<0 sprzeczność, brak rozwiązań
e) 16x² = (x+2)²
16x² = x² + 4x + 4
16x² - x² - 4x - 4 = 0
15x² - 4x - 4 = 0
a = 15
b = -4
c = -4
Δ = b² - 4ac = (-4)² - 4•15•(-4) = 16 + 240 = 256
√Δ = √256 = 16
x1 = (-b-√Δ)/2a
x1 = (-(-4)-16)/2•15 = (4-16)/30 = -12/30 = 2/5
x2 = (-b+√Δ)/2a
x2 = (-(-4)+16)/2•15 = (4+16)/30 = 20/30 = 2/3
h) 2x² = (x+5)²
2x² = x² + 10x + 25
2x² - x² - 10x - 25 = 0
x² - 10x - 25 = 0
a = 1
b = -1
c = -25
Δ = b² - 4ac
Δ = (-1)² - 4•1•(-25) = 1 + 100 = 101
√Δ = √101
x1 = (-b-√Δ)/2a
x1 = (-(-1)-√101)/2•1 = 1-√101/2
x2 = (-b+√Δ)/2a
x2 = (-(-1)+√101)/2•1 = 1+√101/2
