Question

Cho \(\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{d}\) chung minh rang \(\dfrac{a^3+b^3+c^3}{a^3+c^3+d^3}=\dfrac{a}{d}\)

Answer 1

Ta co :\(\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{d}\)=>\(\left(\dfrac{a}{b}\right)^3=\left(\dfrac{b}{c}\right)^3=\left(\dfrac{c}{d}\right)^3\)

=> \(\dfrac{a^3}{b^3}=\dfrac{b^3}{c^3}=\dfrac{c^3}{d^3}=\dfrac{a^3+b^3+c^3}{b^3+c^3+d^3}\) (1)

Mặt khác:\(\dfrac{a^3}{b^3}=\dfrac{a}{b}.\dfrac{b}{c}.\dfrac{c}{d}=\dfrac{a}{d}\) (2)

Tu (1) va (2)

=> \(\dfrac{a^3+b^3+c^3}{b^3+c^3+d^3}=\dfrac{a}{d}\) (dpcm)