câu 52+53
Câu 53:
\(a_2^2=a_1\cdot a_3\)
=>\(\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=k\)
\(a_3^2=a_2\cdot a_4\)
=>\(\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=k\)
=>\(a_2=a_1\cdot k;a_3=a_2\cdot k;a_4=a_3\cdot k\)
=>\(a_2=a_1\cdot k;a_3=a_1\cdot k^2;a_4=a_1\cdot k^3\)
\(\dfrac{a_1^3+a_2^3+a_3^3}{a_2^3+a_3^3+a_4^3}=\dfrac{a_1^3+a_1^3\cdot k^3+a_1^3\cdot k^6}{a_1^3\cdot k^3+a_1^3\cdot k^6+a_1^3\cdot k^9}=\dfrac{1}{k^3}\)
\(\dfrac{a_1}{a_4}=\dfrac{a_1}{a_1\cdot k^3}=\dfrac{1}{k^3}\)
=>\(\dfrac{a_1^3+a_2^3+a_3^3}{a_2^3+a_3^3+a_4^3}=\dfrac{a_1}{a_4}\)
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