Question

câu 52+53

Answer 1

Câu 53:

\(a_2^2=a_1\cdot a_3\)

=>\(\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=k\)

\(a_3^2=a_2\cdot a_4\)

=>\(\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=k\)

=>\(a_2=a_1\cdot k;a_3=a_2\cdot k;a_4=a_3\cdot k\)

=>\(a_2=a_1\cdot k;a_3=a_1\cdot k^2;a_4=a_1\cdot k^3\)

\(\dfrac{a_1^3+a_2^3+a_3^3}{a_2^3+a_3^3+a_4^3}=\dfrac{a_1^3+a_1^3\cdot k^3+a_1^3\cdot k^6}{a_1^3\cdot k^3+a_1^3\cdot k^6+a_1^3\cdot k^9}=\dfrac{1}{k^3}\)

\(\dfrac{a_1}{a_4}=\dfrac{a_1}{a_1\cdot k^3}=\dfrac{1}{k^3}\)

=>\(\dfrac{a_1^3+a_2^3+a_3^3}{a_2^3+a_3^3+a_4^3}=\dfrac{a_1}{a_4}\)