Question

a) 5(y+1)=4

b) jedna trzecia (ulamek tu )(z+6)=4

c) 1-3x=5x-7

d) 5x(4+4x)=5

Answer 1

a]

5(y+1)=4

5y+5=4

5y=4-5

5y=-1

y=-⅕

b]

⅓(z+6)=4  /×3

z+6=12

z=12-6

z=6

c]

1-3x=5x-7

1+7=5x+3x

8x=8

x=8:8

x=1

d]

5x(4+4x)=5  /;5

x(4+4x)=1

4x+4x²-1=0

4x²+4x-1=0

Δ=b²-4ac=16+16=32

√Δ=4√2

x₁=[-b-√Δ]/2a=[-4-4√2]/8=[-1-√2]/2

x₂=[-b+√Δ]/2a=[-4+4√2]/8=(√2-1)/2

 

 

Answer 2

a)

5(y+1) = 4

5y+5 = 4

5y = 4-5

5y = -1  /:5

y = -1/5

 

b)

1/3 *(z+6) = 4  I*3

z+6 = 12

z = 12-6

z = 6

 

c)

1-3x = 5x-7

-3x-5x = -7-1

-8x = -8  /:(-8)

x = 1

 

d)

5x(4+4x) = 5

20x+20x^2 -5 = 0  /:5

4x^2 + 4x -1 = 0

D(delta) = b^2 - 4ac = 16 +16 = 32

VD = 4V2

x1 = (-b-VD)/2a = (-4-4V2)8 = 4(-1-V2)/8 = (-1-V2)/2 = -(V2+1)/2

x1 = (-b+VD)/2a = (-4+4V2)/8 = 4(-1+V2)/8 = (-1+V2)/2 = (V2-1)/2