Question

Cho dãy tỉ số \(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}\)Chứng minh rằng:\(\frac{a^3+b^3+c^3}{b^3+c^3+d^3}=\frac{a}{d}\)

Answer 1

\(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}\Rightarrow\frac{a^3}{b^3}=\frac{b^3}{c^3}=\frac{c^3}{d^3}=\frac{a}{b}.\frac{b}{c}.\frac{c}{d}=\frac{a}{d}=\frac{a^3+b^3+c^3}{b^3+c^3+d^3}\)

=>đpcm

Answer 2

a/b=b/c=c/d

=>a/b.a/b.a/b=b/c.b/c.b/c=c/d.c/d.c/d=a/b.b/c.c/d=a³/b³=b³/c³=c³/d³=a/d=(a³+b³+c³)/(b³+c³+d³)

vậy ..........