Răspuns:
domeniu x∈(0,+∞)
Punctul de intersectie se calculeaza f(x)=g(x)=h(x)
Din h(x)=-xf(x)=>
f(x)= -xf(x)
f(x)+xf(x)=0
f(x)(1+x)=0=>
f(x)=0
sau x=1
f(1)=1²-2/√1+1=1-2+1=0
g(1)=1/√1+(-1)¹={1-1=0
h(1)=-1*f(1)=-1*0=0
f(1)=g(1)=h(1)=0
Punctu;l A(1,0) punct de intersectie
Caz 2 f(x)=0
x²-2/√x+1=0
Substitutie √x=y
x²=(√x)⁴
Ecuatia devine
y⁴-2/y+1=0
y⁵+y-2=0
(y-1)(y⁴+y³+y²+2
y-1=0y=1
A 2 paranteza e o suma de numere strict pozitive deci e strict pozitiva
y=1 solutie
Revii la substitutie
√x=1=>
x=1
Deci (1,0 ) solutie unica
Explicație pas cu pas:
