Question

Cho a,b,c,d là các số khác 0 thỏa mãn : \(b^2=ac;c^2=bd\).

CMR : \(\frac{a^3+b^3-c^3}{b^3+c^3-d^3}=\frac{a}{d}\)

Answer 1

\(b^2=ac\Rightarrow\frac{a}{b}=\frac{b}{c}\)

\(c^2=bd\Rightarrow\frac{b}{c}=\frac{c}{d}\)

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

=> đpcm