\(\dfrac{a}{b}=\dfrac{c}{d}\Rightarrow\dfrac{a}{c}=\dfrac{b}{d}=\dfrac{a-b}{c-d}\Rightarrow\dfrac{a^4}{c^4}=\dfrac{b^4}{d^4}=\left(\dfrac{a-b}{c-d}\right)^4\) ( 1 )
\(\Rightarrow\dfrac{a^4}{c^4}=\dfrac{b^4}{d^4}=\dfrac{a^4+b^4}{c^4+d^4}\) ( 2 )
Từ ( 1 ), ( 2 ) \(\Rightarrow\left(\dfrac{a-b}{c-d}\right)^4=\dfrac{a^4+b^4}{c^4+d^4}\)