Question

Rozwiąż układ równań:

(x-5)2-(x-2y)(x+2y)=(2y-4)2+3

(2x+4)2-(5-3y)2=(2x-3y)(2x+3y)-55

Answer 1

(x-5)²-(x-2y)(x+2y)=(2y-4)²+3

x² - 10x + 25 - x² + 4y² = 4y² - 16y + 16 + 3

-10x + 25 = -16y + 19

-10x + 16y = -6

5x - 8y = 3

 

(2x+4)²-(5-3y)²=(2x-3y)(2x+3y)-55

4x² + 16x + 16 - 25 + 30y - 9y² = 4x² - 9y² - 55

16x + 30y - 9 = -55

16x + 30y = -46

8x + 15y = -23

 

5x - 8y = 3 ------ / * 15

8x + 15y = -23----/ * 8

 

75x - 120y = 45

64x + 120y = -184

-----------------------

139x = -139

x =-1

 

-5 - 8y = 3

-8y = 3 + 5

-8y = 8

y = -1

 

x = - 1

y = -1