Răspuns:
Explicație pas cu pas:
Aplicam Suma Gauss:
x(x+1)/2=55 x²+x=110 x²+x-110=0
x1,2=-1±√1+440/2=-1±21/2
x1=(-1+21)/2=20/2=10
x2=-1-21/2=-11 nu convine x ∈N
Raspuns: x=10
[tex]x \times (x + 1) \div 2 = 55 \\ x {}^{2} + x = 110 \\ x {}^{2} + x - 110 = 0 \\ (x - 10) \times (x + 11) = 0 \\ x = 10[/tex]
Verificare :
1+2+3+4+5+6+7+8+9+10=10(10+1)/2=5×11==》55