Question

Rozwiąż równania :

a) ( X- 1)² - (X+4)²= 2x+1

b) ( X+1)²+ (x-3)(X+3)-2=2(x-1)²

c) (X+3)²-(4-x)(4+X)=2(x-1)²+1

Answer 1

a)

( X- 1)² - (X+4)²= 2x+1

 x² - 2x + 1 - x² - 8x - 16 = 2x + 1

-10x - 15 = 2x + 1

-10x - 2x = 1 + 15

-12x = 16

x = -16/12

x = - 4/3

x = -1 i 1/3

 

b)

( X+1)²+ (x-3)(X+3)-2=2(x-1)²

 x² + 2x + 1 + x² - 9 - 2 = 2(x² - 2x + 1)

2x² + 2x - 10  = 2x² - 4x + 2

2x + 4x = 2 + 10

6x = 12

x = 2

 

c)

(X+3)²-(4-x)(4+X)=2(x-1)²+1

x² + 6x + 9 - 16 + x² = 2(x² - 2x + 1) + 1

2x² + 6x - 7 = 2x² - 4x + 2 + 1

6x + 4x = 3 + 7

10x = 10

x = 1