Question

Rezolvaţi in mulţimea numerelor reale ecuatiile:
2+5+8+11+...+x=155

Answer 1

Cred ca se rezolva cu progresie aritmetica
suma=155
r=3
 an=x
an=a1+r(n-1)⇒x=2+3(n-1)⇒3n=x-2+3⇒n=(x+1)/3
s=(a1+an)*n/2
 
155=[(2+x)*(x+1)/3]/2
155=(2x+2+x²+x)/6   |*6
930=x²+3x+2
x²+3x-928=0
Δ=3721
x1=(-3+61)/2=58/2=29
x2=-64/2=-32
verificare:
 s1=(2+29)*10/2=31*5=155 (A)
s2=(2-32)*(-31/3)/2 ≠155
  
      Solutia={29}