Question

Se considera functiile f:R->R,f(x)=x la patrat -2x+1,g(x)=-x la patrat+1.Sa se determine solutiile reale ale ecuatiei f(x)=g(x)

Answer 1

f(x)=x²-2x+1
g(x)=-x²+1
f(x)=g(x)
x²-2x+1=-x²+1
x²-2x+1+x²-1=0
2x²-2x=0

Metoda 1:
Observi descompunerea:
2x(x-1)=0
2x=0 => x1=0
x-1=0 => x2=1

Metoda 2:
Calculam cu delta:
2x²-2x=0
Δ=(-2)²-4*2*0=4
√Δ=√4=2
x1=2+2/4=4/4=1
x2=2-2/4=0/4=0

Prin ambele metode, avem aceleasi solutii pentru x:
x∈{0;1}