Ta có:
\(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}=\frac{a-b}{c-d}\Rightarrow\frac{a^4}{c^4}=\left(\frac{a-b}{c-d}\right)^4\left(1\right)\)
Từ \(\frac{a}{c}=\frac{b}{d}\Rightarrow\frac{a^4}{c^4}=\frac{b^4}{d^4}=\frac{a^4+b^4}{c^4+d^4}\left(2\right)\)
Từ ( 1 ) và ( 2 ) => \(\left(\frac{a-b}{c-d}\right)^4=\frac{a^4+b^4}{c^4+d^4}\)
\(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a^4}{b^4}=\frac{c^4}{d^4}=\frac{a^4-c^4}{b^4-d^4}=\left(\frac{a-c}{b-d}\right)^4\left(1\right)\)
\(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a^4}{b^4}=\frac{c^4}{d^4}=\frac{a^4+c^4}{b^4+d^4}\left(2\right)\)
từ (1) và (2) --> \(\left(\frac{a-c}{b-d}\right)^4=\frac{a^4+c^4}{b^4+d^4}\left(đpcm\right)\)
