Ta có : \(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}=\frac{a+b}{c+d}\Rightarrow\frac{a^3}{c^3}=\frac{b^3}{d^3}=\left(\frac{a+b}{c+d}\right)^3\) (1)
Mà \(\frac{a^3}{c^3}=\frac{b^3}{d^3}=\frac{a^3+b^3}{c^3+d^3}\)(TC DTSBN) (2)
Từ (1) ; (2) => \(\left(\frac{a+b}{c+d}\right)^3=\frac{a^3+b^3}{c^3+d^3}\) (đpcm)