Question

Rozwiąż układ równań.

IyI - to moduł

Answer 1

(x - 2)² + y² = 18

|y| + x = 2

 

|y| = 2 - x      

D: 2 - x > 0

        -x > - 2

         x <  2

D = (-oo, 2)

y = 2 - x      lub   y = -(2 - x)

                         y = x - 2

 

(x - 2)² + y² = 18           lub      (x - 2)² + y² = 18

y = 2 - x                                   y = x - 2

 

(x - 2)² + (2 - x)² = 18           lub  (x - 2)² + (x - 2)² = 18

y = 2 - x                                       y = x - 2

 

x² - 4x + 4 + 4 - 4x + x² = 18   lub    2(x - 2)² = 18

y = 2 - x                                          y = x - 2

 

2x² - 8x + 8 = 18                     lub    (x - 2)² = 9

y = 2 - x                                           y = x - 2

 

2x² - 8x - 10 = 0                      lub   (x - 2)² = 3²

y = 2 - x                                           y = x - 2

 

x² - 4x - 5 = 0                         lub     x - 2 = 3  lub   x - 2 = -3

y = 2 - x                                           y = x - 2

 

Δ = 16 + 20 = 36                                x = 5 ∉ D     lub     x = - 1 ∈ D

√Δ = 6                                               y = x - 2

x1 = (4 - 6)/2 = -2/2 = -1 ∈ D

x2 = (4 + 6)/2 = 10/2 = 5  ∉ D                        x = -1

                                                                    y = -1 - 2 = -3

 

x1 = -1

y1 = 2 - (-1) = 2 + 1 = 3

 

odp. x = -1 to y = 3   lub   x = -1 to y = -3