a_1
a_2=a_1*q
a_3=a_1*q^2
\left \{ {{a_1*a_2*a_3=216} \atop {a_1+a_2+a_3=21}} \right.
\left \{ {{a_1*a_1*q*a_1*q^2=216} \atop {a_1+a_1*q+a_1*q^2=21}} \right.
\left \{ {{{a_1}^3*q^3=6^3 } \atop {a_1+a_1q+a_1q^2=21}} \right.
\left \{ {{a_1q=6 } \atop {a_1+6+a_1q^2=21 \ |-6}} \right.
\left \{ {{a_1=\frac{6}{q}} \atop {a_1q^2+a_1=15}} \right.
a_1(q^2+1)=15
\frac{6}{q}(q^2+1)=15 \ |:3
\frac{2}{q}(q^2+1)=5 \ |*q
2(q^2+1)=5q
2q^2+2-5q=0
2q^2-5q+2=0
\Delta=25-4*2*2=9
\sqrt\Delta=3
q_1=\frac{5-3}{2*2}=\frac{2}{4}=\frac{1}{2}
q_2=\frac{5+3}{4}=2
a_1=\frac{6}{q}
dla q = 1/2
a_1=\frac{6}{\frac{1}{2}}=12
a_2=a_1*q=12*\frac{1}{2}=6
a_3=a_2*q=6*\frac{1}{2}=3
dla q = 2
a_1=\frac{6}{2}=3
a_2=3*2=6
a_3=6*12=12
Jest to ciąg: 12, 6, 3 lub 3, 6, 12.
6+3+12=21
6312=216