Question

Rezolvati ecuatia 1+2+3+…x=55

Answer 1

aplici formula
1+2+3+...+n=n(n+1)/2

n(n+1)/2=55
n(n+1)=55*2
n(n+1)=110
n^2+n=100
n^2+n-110=0

ec de gr 2, dar n trebuie sa fie doar numar natural, mai mare ca 0

delta= b^2-4ac 
delta=1^2-4*1*(-110)
delta=1+440
delta=441
radical din delta= 21

n1=-b+ radical delta/ 2a
n1=-1+21/2
n1=20/2
n1=10

nr nu se poate, pt ca da cu minus
n2=-b-rad delta/2a
n2=-1-21/2
n2=-22/2
n2=-11

Answer 2

1 + 2 + 3 + ... + x = 55
$S_{x} = \frac{(1+x)*x}{2} = 55$
x+ x² = 110
x²+x-110=0
Δ = 1+440 = 441
x₁ = $\frac{-1+21}{2} = 10$ 
x₂ = $\frac{-1-21}{2} = -11$ nu convine x>0
             x = 10