Question

Rozwiąż i sprawdz następujące równania

a)x(x-2)+2-x2=8+x

b) x(x-8)+4=x2+2(x-3)

c) 2(x2+3x+4)-2x2=18+x

d) 2(x2-5x-6)=x(x+2)+x2

e) 2(y-7+y2)-y(2y-3)=3(y-2)

f) 5(x-1)-x(x-4)+x(x-2)=2

Pomóżcie

x2 lub y2 oznacza y lub x do kwadratu

Answer 1

a] x[x-2]+2-x^=8+x
   x^-2x+2-x^=8+x
   x^-2x-x^-x=8-2
    -3x=6    /:[-3]
     x= -2
b] x[x-8]+4=x^+2[x-3]
    x^-8x+4=x^+2x-6
    x^-8x-2x-x^= -6-4
      -10x= -10    /:[-10]
        x=1
c] 2[x^+3x+4]-2x^=18+x
   2x^+6x+8-2x^=18+x
   2x^+6x-2x^-x=18-8
   5x=10     /:5
   x=2
d] 2[x^-5x-6]=x[x+2]+x^
    2x^-10x-12=x^+2x+x^
    2x^-10x-x^-2x-x^=12
     -12x=12   /:[-12]
       x= -1
e] 2[y-7+y^]-y[2y-3]=3[y-2]
   2y-14+2y^-2y^+3y=3y-6
   2y+2y^-2y^+3y-3y= -6+14
    2y=8    /:2
     y=4
f] 5[x-1]-x[x-4]+x[x-2]=2
   5x-5-x^+4x+x^-2x=2
    5x-x^+4x+x^-2x=2+5
    7x=7      /:7
    x=1

 

 

x^ lub y^ oznacza x lub y do kwadratu

Answer 2

a) x(x - 2) + 2 - x² = 8 + x

x² - 2x + 2 - x² = 8 + x

2 - 8 = x + 2x

-6 = 3x

x = -2

 

spr.

-2(-2 - 2) + 2 - (-2)² = 8 + (-2)

4 + 4 + 2 - 4 = 8 - 2

10 - 4 = 6

6 = 6

 

b)

x(x - 8) + 4 = x² + 2(x - 3)

x² - 8x + 4 = x² + 2x - 6

4 + 6 = 2x + 8x

10 = 10x

x = 1

 

spr

1(1 - 8) + 4 = 1² + 2(1 - 3)

1 - 8 + 4 = 1 + 2 - 6

-3 = -3

 

c)

2(x² + 3x + 4) - 2x² = 18 + x

2x² + 6x + 8 - 2x² = 18 + x

5x = 10

x = 2

 

2(2² + 6 + 4) - 2 · 2² = 18 + 2

8 + 12 + 8 - 8 = 20

20 = 20

 

d)

2(x² - 5x - 6) = x(x + 2) + x²

2x² - 10x - 12 = x² + 2x + x²

2x² - 12 = 2x² + 2x + 10x

-12 = 12x

x = -1

 

spr

2[(-1)² - 5 · (-1) - 6] = -1(-1 + 2) + (-1)²

2]1 - (-5) - 6] = 1 - 2 + 1

2 + 10 - 12 = 0

0 = 0

 

e)

2(y - 7 + y²) - y(2y - 3) = 3(y - 2)

2y - 14 + 2y² - 2y² + 3y = 3y - 6

5y - 14 = 3y - 6

2y = 8

y = 4

 

spr

2(4 - 7 + 16) - 4(8 - 3) = 3(4 - 2)

8 - 14 + 32 - 32 + 12 = 12 - 6

-6 + 12 = 12 - 6

6 = 6

 

 

f)

5(x - 1) - x(x - 4) + x(x - 2) = 2

5x - 5 - x² + 4x + x² - 2x = 2

7x = 7

x = 1

 

spr

5(1 - 1) - 1(1 - 4) + 1(1 - 2) = 2

5 - 5 - 1 + 4 + 1 - 2 = 2

2 = 2