a_1+a_3=52
a_2^2=100
…
wzory
a_n=a_1q^{n-1}
a_n^2=a_{n-1}*a_{n+1}
…
a_2^2=a_1*a_3=100
\left \{ {{a_1+a_3=52} \atop {a_1*a_3=100}} \right.
\left \{ {{a_1=52-a_3} \atop {(52-a_3)*a_3=100}} \right.
\left \{ {{a_1=52-a_3} \atop {(52a_3-a_3^2=100}} \right.
\left \{ {{a_1=52-a_3} \atop {(-a_3^2+52a_3-100=0}} \right.
-a_3^2+52a_3-100=0
\Delta=b^2-4ac=2704-400=2304
\sqrt{\Delta}=48
a_{3_1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-52-48}}{-2}=50
a_{1_1}=52-50=2
a_{3_2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-52+48}}{-2}=2
a_{1_1}=52-2=50
…
I
a_3=50
a_1=2
a_3=a_1q^2
50=2q^2
q^2=25
q=5
a_2=a_1q=2*5=10
…
II
a_3=2
a_1=50
a_3=a_1q^2
2=50q^2
q^2=0,04
q=0,2
a_2=a_1q=50*0,2=10
mam nadzieję, że nic nie pomyliłam…