Odpowiedzi

2010-03-24T21:20:19+01:00
A) 2x-1/x+1=2/x
x(2x-1)=2(x+1)
2x²-x=2x+2
2x²-x-2x-2=0
2x²-3x-2=0
a=2
b= -3
c= -2
Δ= b²-4ac
Δ= (-3)²-4*2*(-2)
Δ= 9+16
Δ=25
√Δ=5

x1= -b-√Δ / 2a
x1= 3-5 / 2*2
x1= -2 / 4
x1= -½

x2= -b+√Δ / 2a
x2= 3+5 / 2*2
x2= 8/4
x2= 2

b) x-3/x=5-x/x+1
(x-3)(x+1)=x(5-x)
x²+x-3x-3=5x-x²
x²+x²+x-3x-5x-3=0
2x²-7x-3=0
a=2
b= -7
c= -3
Δ= b²-4ac
Δ= (-7)²-4*2*(-3)
Δ= 49+24
Δ=73
√Δ= √73

x1= -b-√Δ / 2a
x1= 7-√73 / 2a
x1= 7-√73 / 2*2
x1= 7-√73 / 4

x2= -b+√Δ / 2a
x2= 7+√73 / 2*2
x2= 7+√73 / 4

c) x/3x-2=3x-2/x+4
x(x+4=(3x-2)(3x-2)
x²+4x=9x²-6x-6x+4
x²-9x²+4x+6x+6x-4=0
-8x²+16x-4=0
a= -8
b= 16
c= -4
Δ= b²-4ac
Δ= 16²-4*(-8)*(-4)
Δ=256-128
Δ=128
√Δ=√128

x1= -b-√Δ / 2a
x1= -16-√128 / 2*(-8)
x1= -16-√128 / -16

x2= -b+√Δ / 2a
x2= -16+√128 / 2*(-8)
x2= -16+√128 / -16
2010-03-24T21:27:23+01:00
A)2/x-1/x+1+2/x
1/x+1=2/x
-2/x+1/x=-1
1/x=1
x=1

b)1/x-3/x=5-1+1
-2/x=4/:-2
x=-2