Question

Fie functiile f,g:R->R , f(x)=x^2-x+1 si g(x)=x+4.Sa se calculeze coordonatele punctelor de intersectie a graficelor functiilor f si g.

Answer 1

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Answer 2

Consideram M(y;z) astfel incat x²-x+1=y si x+4=y ⇔x²-x+1=x+4 ⇔x²-x+1-x-4=0 ⇔x²-2x-3=0.
x²-2x-3=0 ⇒Δ=b²-4ac=(-2)²-4·1·(-3)=4-(-12)=4+12=16
Deoarece Δ>0 ⇔16>0 atunci solutia ecuatiei poate lua doua valori
x₁,₂=-b+-√Δ/2a=2+-√16/2 ⇒x₁=2+4 /2=3 si x₂=2-4 /2=-1
Asadar S={-1;3}
Daca x=3 ⇒y=3²-3+1=7 dar y=z ⇒z=7 ⇒M(7;7);
Daca x=-1 ⇒y=(-1)²+1+1=3 dar y=z ⇒z=3 ⇒M(3;3);