EX 5 DE LA SUB 2 VA ROG​

Rezolvare:

x²-|x-1|= 2x-1

x²= 2x-1+|x-1|

x²-2x+1=|x-1|

caz l : x-1 = x²-2x+1 |+1

x=x²-2x+2 |+2x

3x= x²+2 => x= 2

caz ll : -x+1= x²-2x+1 |-1

-x= x²-2x |+2x

x= x² =>x= 1

Raspuns: x= { 1,2}

1. x-1>=0

[tex] {x}^{2} - x + 1 = 2x - 1 \\ {x}^{2} - 3x + 2 = 0 \\ x = 2 \: si \: x = 1[/tex]

2. x-1<0

[tex] {x}^{2} + x - 1 = 2x - 1 \\ {x}^{2} -x = 0 \\ x(x - 1) = 0 \\ x = 0 \: si \: x = 1[/tex]

In cazul 1 am aflat x folosind formula X1,2=

[tex] \frac{ - b + - \sqrt{ {b}^{2} - ac } }{2a} [/tex]

unde a=1 b=-3 c=2 adică coeficienții