a)Presupunem ca numerele a, b si c sunt naturale.Daca aceste numere sunt in progresie geometrica atunci: [tex]a=a, b=a\cdot q, c=a\cdot q^2[/tex]
Sistemul se scrie:
[tex]a+aq+aq^2=26\\
\frac{1}{a}+\frac{1}{aq}+\frac{1}{aq^2}= \frac{13}{18} \\
\frac{1}{a} (1+\frac{1}{q}+\frac{1}{q^2})= \frac{13}{18}\\
a(1+q+q^2)=26=>1+q+q^2= \frac{26}{a} \\
\frac{1}{a}\cdot\frac{q^2+q+1}{q^2}= \frac{13}{18} => \frac{1}{a} \cdot \frac{1}{q^2} \cdot \frac{26}{a} =\frac{13}{18}=>a\cdot q=6[/tex]
[tex]a+6+6q=26\\
a+6q=20[/tex]
Avem doua situatii:
a=2,q=3,b=6,c=18
sau
a=18.q=1/3,b=6,c=2
