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a) z= 4a-7
z+7= 4a
z/4 + 7/4 = a
b)t= 1-a/3
t-1=-a/3
3t-3=-a
-3t+3=a
c)f= ab/b+1
f-1=ab/b
(f-1)b=ab
f-1=a
d)y= 3(a-2)/1-b
y+b=3a-6
y+b+6=3a
(y+b+6)/3=a
2. rozwiąż równanie :
a) x/a +x²=0
ax²+x=0
Δ=1
a₁=0 a₂=-a
b)x²+6x+9=0
Δ=36-36=0
x=-3
c)x²+6x=7
x²+6x-7=0
Δ=36+28=64
pierwiastek z Δ=8
x₁=1 x₂=-7
d)3x²+2x-2=0
Δ=4+24=28
pierwiastek z Δ=2√14
x₁=(-2+2√14)/6=(-1+√14)/3
x₂=(-1-√14)/3
e)2x= 5x²+1
-5x²+2x-1=0
Δ=4-20=-16 delta mniejsza od zera czyli brak rozwiązań tego równania
f)2-4x=3x²
-3x²-4x+2=0
Δ=16+24=40
x₁=(4+2√10)/-6=-(2+√10)/3
x₂=-(2-√10)/3
a) z=4a-7
z+7=4a / :4
z+7
⁻⁻⁻⁻⁻⁻ = a
4
b) t=1-a/3
3t=1-a
-3t+1=a
c) f=ab/b+1
f(b+1)=ab/:b
f(b+1)
⁻⁻⁻⁻⁻⁻⁻⁻⁻ =a
b
d)y=2(a-2)/1-b
y(1-b)=3(a-2)/:3
y(1-b)
⁻⁻⁻⁻⁻ = a-2
3
y(1-b)
⁻⁻⁻⁻⁻⁻ -2 = a
3
zad.2
b) Δ=b*b - 4ac
Δ=6*6 - 4*9*1
Δ=36-36
Δ=0
x=b/2a
x=6/2=3
c)Δ=b²-4ac
Δ=6²-4*(-7)81
Δ=36+28=64
x₁=-b-√Δ/2a
x₁=-6-8/2
x₁=-7
x₂=-b+√Δ/2a
x₂=-6+8/2
x₂=1
d)Δ=b²-4ac
Δ=2²-4*3*(-2)
Δ= 4+24=28≈5,29
x₁=-b-√Δ/2a
x₁=-2-5,29/6
x₁=-7.29/6=1.21
x₂=-b+√Δ
x₂=-2+5.29/6
x₂=3,29/6=0.54
f) Δ=-4²-4*(-3)*2=16+24=40≈6.3
x₁=4-6.3/-6=2.3/-6=-38
x₂=4+6.3/-6=10.3/-6=-1.71
e)Δ=-2*(-2)-4*5*1=4-20=16
x₁=2-4/10=-1/5
x₂=6/10=3/5