Question

[Gia Khang]

C/m rằng,nếu a/b=b/c=c/d thì a³+b³+c³/b³+c³+d³=a/d

Answer 1

[Xyz OLM]

Ta có : \(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}\)

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

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

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

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

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

Answer 2

[Gia Khang]

Cảm ơn bạn Xyz nhiều