Question

Rozwiąż równanie.

a) 2x(x-1) = 2x²+4

b) 1/2x(4-6x) - 1/3x(9x-12) = -2x(3x+1)

c) (y-2)(3+2y)-y² = y²+5

d) (x+2)² = x²

e) (2-3x)² - (1+2x)² - 3x² = 2x²

f) (x+2)² = x² - 2

Dam naaj.

Answer 1

a) 2x(x-1) = 2x²+4

2x² - 2x = 2x² + 4

-2x = 4

x = -2

b) 1/2x(4-6x) - 1/3x(9x-12) = -2x(3x+1)

2x - 3x² - 3x² + 4x = -6x² - 2x

- 6x² + 6x = -6x² - 2x

6x = - 2x

x = 0

c) (y-2)(3+2y)-y² = y²+5

3y + 2y² - 6 - 4y -y² = y² + 5

-y + y² - 6 = y² + 5

- y = 11

y = -11

d) (x+2)² = x²

x² + 4x + 4 = x²

4x = -4

x = -1

e) (2-3x)² - (1+2x)² - 3x² = 2x²

4 - 12x + 9x² - (1 + 4x + 4x²) - 3x² = 2x²

4 - 12x + 9x² - 1 - 4x - 4x² = 5x²

4 - 12x - 1 - 4x = 0

3 = 16 x

x = 3/16

f) (x+2)² = x² - 2

x² + 4x + 4 = x² - 2

4x + 4 = -2

4x = - 6

x = -6/4

Answer 2

a) 2x(x-1) = 2x²+4
2x²-2x-2x²-4=0

-2x-4=0

-2x=4

x=-2

b) 1/2x(4-6x) - 1/3x(9x-12) = -2x(3x+1)
2x-3x²-3x²+4x=-6x²-2x

6x-6x²=-6x²-2x

6x=-2x

6x+2x=0

8x=0

x=0 

c) (y-2)(3+2y)-y² = y²+5

3y+2y²-6-4y-y²-y²-5=0

-y-11=0

-y=11

y=-11

d) (x+2)² = x²

x²+4x+4-x²=0

4x=-4

x=-1

e) (2-3x)² - (1+2x)² - 3x² = 2x²

4-12x+9x²-(1+4x+4x²)-3x²-2x²=0

4-12x+9x²-1-4x-4x²-5x²=0

-16x+3=0

-16x=-3

x=3/16 

f) (x+2)² = x² - 2

x²+4x+4-x²+2=0

4x+6=0

4x=-6

x=-6/4

x=-3/2 

 

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