Question

Rozwiąż równanie. a) (x+2)²=x², b) (x=1)²=x²-1, c) (x+4)²=x(6+x), d) (3x+2)²=x(-2+9x)

Answer 1

a) (x + 2)² = x²

x² + 4x + 4 = x²

4x = - 4

x = - 1

 

b) (x - 1)² = x² - 1

x² - 2x + 1 = x² - 1

-2x = - 2

x  = 1

 

c) (x + 4)² = x(6 + x)

x² + 8x + 16 = 6x + x²

2x = - 16

x = - 8

 

d) (3x + 2)² = x(-2 + 9x)

9x² + 12x + 4 = - 2x + 9x²

14x = - 4

x = - 2/7

Answer 2

a) (x + 2)² = x²

x² + 2² = x²

x² + 4 = x²

√x² + √4 = √x²

x + 2 = x

x - x = -2

0 = -2

 

b) (x + 1)² = x² - 1

x² + 1 = x² - 1

x² - x² = -1 -1

0 = -2

 

c) (x + 4)² = x(6 + x)

x² + 16 = 6x + x²

x² - x² = 6x - 16

0 = 6x - 16

16 = 6x

x = 2,(6)

 

d) (3x + 2)²=x(-2 + 9x)

3x² + 4 = -2x + 9x²

-2x = 3x² + 4 - 9x²

-2x = 4 - 6x²

-x = 2 - 3x²

x = 3x² - 2