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2010-01-05T18:55:37+01:00
A)6x²+x-1=0_____a=6____b=1_____c=-1
Δ=b²-4ac=1²-4*6*(-1)=1+24=25
x₁=-b+√Δ/2a=-1+√25/2*6=-1+√25/12
x₂=-b-√Δ/2a=-1-√25/2*6=-1-√25/12

b)5x²+9x-14=0____a=5___b=9____c=-14
Δ=b²-4ac=9²-4*5*(-14)=81+280=361
x₁=-b+√Δ/2a=-9+19/2*5=¹⁰/₁₀=1
x₂=-b-√Δ/2a=-9-19/2*5=²⁸/₁₀=2⁸/₁₀=2⁴/₅

c)-x²-2x-1=0_____a=-1____b=-2_____c=-1
Δ=b²-4ac=(-2)²-4*(-1)*(-1)=4-4=0
____b_____-2______-2
x₀=-~~~~=-~~~~~~=-~~~~~~=-1
____2a____2*(-1)___-2
mam nadzieje ze rozczytasz to jest ułamek przed tymi ~~~~~ stoi znak -
2010-01-05T20:07:32+01:00
A)6x² + x -1 = 0
Δ = b²-4ac
Δ = 1² - 4 * 6 * (-1)
Δ = 1+ 24 = 25
√Δ = 5
x₁=-b +√Δ/2a =-1 + 5 /12 = -4/12 = - 1/3
x₂=-b - √Δ/2a =-1 - 5 /12 = -6/ 12 = -1/2

b)5x²+9x-14=0
Δ = b² - 4ac
Δ = 9² -4*5*(-14)=81+140 = 221
√Δ = 11
x₁= -b + √Δ/2a = -9 + 11 /2*5 = -2/ 10 = -1/5
x₂= -b - √Δ/2a = -9- 11/2*5 = -20/10 = -2

c)-x²-2x-1=0
Δ = b² - 4ac =
Δ = (-2)² - 4 * (-1) * (-1) =
Δ = 4 + 4 = 8
√Δ = √4*2
√Δ = 2√2
x₁= -b + √Δ/2a = 2 + 2√2 / -2 = 2 * (1 + √2) /-2 = - ( 1 + √2) = 1 - √2
x₂= -b - √Δ/2a = 2 - 2√2 / -2 = 2 * (1 - √2) /-2 = - (1 - √2) = 1 +√2