Odpowiedzi

2009-11-06T18:56:23+01:00
(2x+7)/(3x+8) =5. x musi byc różne od -8/3
2x +7 = 5*(3x+8)
2x +7 =5*3x +5*8
2x +7 = 15x + 40
2x -15x =40 -7
- 13x =33
x = - 33/13
Odp. x = -33/13

(2x -5)/(x-1) = 6x/(3x +2) , x musi być różne od 1 oraz -2/3
(2x -5)(3x +2) = 6x*(x - 1)
6x^2 +4x - 15x -10 = 6x^2 -6x
6x^2 +4x -15x +6x -6x^2 -10 =0
-5x = 10
x = 10:(-5) = -2
Odp. x = -2

(x^2 -7)/2x = x-4
x musi być różne od 0

x^2 -7 =2x*(x-4)
x^2 - 7 = 2x^2 - 8x
2x^2 -x^2 -8x +7 = 0
x^2 -8x + 7 = 0
delta =(-8)^2 -4*1*7 =64 -28 =36
pierwiastek z delty = 6
x1 =(8 -6)/2 =2/2 = 1
x2 =(8+6)/2 =14/2 = 7
Odp. x = 1 lub x =7
2009-11-06T18:57:03+01:00
(2x-5)(3x+2)=6x(x-1)
6x²+4x-15x-10=6x²-6x
6x²-6x²+6x+4x-15x=10
-5x=10/(-5)
x=-2


2x(x-4)=x²-7
2x²-8x=x²-7
x²-8x+7=0
Δ=b²-4ac
Δ=(-8)²-4*1*7
Δ=36
√Δ=6

x₁=(8-6)/2
x₁=1
x₂=(8+6)/2
x₂=7
2009-11-06T19:01:53+01:00
2x + 7/3x + 8 = 5 ( mnożymy równanie przez 3x + 8 )
2x + 7 = 5(3x + 8 ) ( mnożymy 3x + 8 przez 5 )
2x + 7 = 15x + 40
2x - 15X = 40 - 7
- 13X = 33
X = -33/13

2x - 5/x - 1 = 6x/3x + 2 ( wspólny mianownik = (x - 1)(3x + 2)
(2x - 5)(3x + 2) = 6x ( x - 1)
6x² - 15x + 4x - 10 = 6x² - 6x
6x² - 6x² - 15x + 6x = 10
- 9x = 10
x = -10/9

x² - 7/2x = x - 4 ( mnożymy przez 2x)
x² - 7 = 2x ( x - 4 )
x² - 7 = 2x² - 2x
x² - 2x² + 2x = 7
- x² + 2x - 7 = 0
x² - 2x + 7 = 0
Δ = 4 + 28
Δ = 32
√Δ = √32 = 4√2
x₁ = - b - √Δ/2a = 2 - 4√2/2 = 1 - 2√2
x₂ = - b + √Δ/2a = 2 + 4√2/2 = 1 + 2√2