Ответ: q=5.
Пошаговое объяснение:
S₃=31 b₁+b₃=26 q=?
b₁+b₃=b₁+b₁q²=b₁*(1+q²)=26
b₁=26/(1+q²)
Sn=b₁*(qⁿ-1)/(q-1)
S₃=26*(q³-1)/((q²+1)(q-1))=31
26*(q³-1)=31*(q²+1)*(q-1)
26q³-26=31*(q³-q²+q-1)
26q³-26=31q³-31q²+31q-31
5q³-31q²+31q-5=0
(5q³-5)-(31q²-31q)=0
5*(q³-1)-31q(q-1)=0
5*(q-1)*(q²+q+1)-31q*(q-1)=0
(q-1)*(5*(q²+q+1)-31q)=0
q-1=0
q=1 ∉
5q²+5q+5-31q=0
5q²-26q+5=0 D=576 √D=24
q₁=0,2 ∉ q₂=5.
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Verified answer
Ответ: q=5.
Пошаговое объяснение:
S₃=31 b₁+b₃=26 q=?
b₁+b₃=b₁+b₁q²=b₁*(1+q²)=26
b₁=26/(1+q²)
Sn=b₁*(qⁿ-1)/(q-1)
S₃=26*(q³-1)/((q²+1)(q-1))=31
26*(q³-1)=31*(q²+1)*(q-1)
26q³-26=31*(q³-q²+q-1)
26q³-26=31q³-31q²+31q-31
5q³-31q²+31q-5=0
(5q³-5)-(31q²-31q)=0
5*(q³-1)-31q(q-1)=0
5*(q-1)*(q²+q+1)-31q*(q-1)=0
(q-1)*(5*(q²+q+1)-31q)=0
q-1=0
q=1 ∉
5q²+5q+5-31q=0
5q²-26q+5=0 D=576 √D=24
q₁=0,2 ∉ q₂=5.