Ta có \(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}=\frac{a+b-c}{b+c-d}\)(dãy tỉ số bằng nhau)
=> \(\left(\frac{a}{b}\right)^3=\left(\frac{b}{c}\right)^3=\left(\frac{c}{d}\right)^3=\left(\frac{a+b-c}{b+c-d}\right)^3\)
=> \(\frac{a^3}{b^3}=\frac{b^3}{c^3}=\frac{c^3}{d^3}=\left(\frac{a+b-c}{b+c-d}\right)^3\)
=> \(\frac{a^3}{b^3}=\frac{b^3}{c^3}=\frac{c^3}{d^3}=\frac{a^3+b^3+c^3}{b^3+c^3+d^3}=\left(\frac{a+b-c}{b+c-d}\right)^3\)(dãy tỉ số bằng nhau)
=> \(\frac{a^3+b^3+c^3}{b^3+c^3+d^3}=\left(\frac{a+b-c}{b+c-d}\right)^3\)(đpcm)