Question

1. Rozwiąż równanie

a ) ( x - 3 ) ² + 3 x = x ² + 6x

b) | x + 3 | - 2 | = 5

c) x ² - 3 = ( x + 2)² + 3x

d) | x + 2 | - 5 | = 3

Answer 1

a ) ( x - 3 ) ² + 3 x = x ² + 6x

       x² -6x + 9 +3x = x² +6x

       x² - x² -6x -6x +3x + 9 = 0

       -9x = -9   /÷ (-9)

          x = 1

 

b)  | x + 3 | - 2 | = 5

        x + 3 + 2 = 5

        x + 5 = 5

        x = 5 - 5

          x = 0

 

c)  x ² - 3 = ( x + 2)² + 3x

      x ² - 3 = x² + 4x + 4 + 3x

      x² - x² -4x -3x = 4 + 3

       -7x = 7      /÷ (-7)

          x = -1

 

d)  | x + 2 | - 5 | = 3

       x + 2 + 5 = 3

       x + 7 = 3

       x = 3 - 7

       x = -4