a)Từ gt: \(a^2_2=a_1a_3\Rightarrow\dfrac{a_1}{a_2}=\dfrac{a_2}{a_3}\)
\(a^2_3=a_2a_4\Rightarrow\dfrac{a_2}{a_3}=\dfrac{a_3}{a_4}\)
\(\Rightarrow\dfrac{a_1}{a_2}=\dfrac{a_2}{a_3}=\dfrac{a_3}{a_4}\)
\(\Rightarrow\dfrac{a^3_1+a^3_2+a^3_3}{a^3_2+a^3_3+a^3_4}=\dfrac{a_1}{a_2}.\dfrac{a_2}{a_3}.\dfrac{a_3}{a_4}=\dfrac{a_1}{a_4}\)
theo tính chât của dãy tỉ số bằng nhau
\(\)\(\dfrac{a^3_1+a^3_2+a^3_3}{a^3_2+a^3_3+a^3_4}=\dfrac{a_1}{a_4}\)
b: \(S=\dfrac{x}{y+z}+\dfrac{y}{z+x}+\dfrac{z}{x+y}\)
\(=\dfrac{x}{y+z}+\dfrac{x}{y+z}+\dfrac{x}{y+z}\)
\(=\dfrac{3x}{y+z}\)
