Question

*Sa se rezolve urmatoarele sisteme de ecuatii : a) X-Y-5=0.
Y=X²-3X-1.

b) 2X+Y+1=0.
Y=X² -5X+4.
*Vreau rezolvarile complete va rog !

Answer 1

Sper sa fie bine. :)

Answer 2

$\it \left \{ {{x-y-5=0} \atop {y=x^{2}-3x-1}} \right. \rightarrow \left \{ {{x-5=y} \atop {x^{2}-3x-1=y}} \right. \rightarrow x-5 = x^{2}-3x-1 \\ \\ x^{2}-3x-x-1+5 =0 \rightarrow x^{2}-4x+4=0 \rightarrow (x-2)^{2}=0 \rightarrow x=2 \\ \\ x-5 = y \rightarrow y=2-5=-3. \\ \\ \\ \left \{ {{2x+y+1=0} \atop {y=x^{2}-5x+4}} \right. \rightarrow \left \{ {{y=-1-2x} \atop {y=x^{2}-5x+4}} \right. \rightarrow -1-2x=x^{2}-5x+4\\ \\ x^{2}-5x+2x+4+1= 0 \rightarrow x^{2}-3x+5=0 \\ \\ delta=(-3)^{2}-4*5*1 \ \textless \ 0 (nu \ avem \ solutii \ in \ R )$