\(\dfrac{a}{b}=\dfrac{c}{d}=\dfrac{a}{c}=\dfrac{b}{d}\)
Áp dụng t/c dãy tỉ số bằng nhau:
\(\dfrac{a}{b}=\dfrac{c}{d}=\dfrac{a}{c}=\dfrac{b}{d}=\dfrac{a+b}{c+d}=\dfrac{\left(a+b\right)^3}{\left(c+d\right)^3}\left(1\right)\\ \Rightarrow\dfrac{a}{c}=\dfrac{b}{d}=\dfrac{a^3}{c^3}=\dfrac{b^3}{d^3}=\dfrac{a^3+b^3}{c^3+d^3}\left(2\right)\\ \left(1\right)\left(2\right)\Rightarrow\dfrac{\left(a+b\right)^3}{\left(c+d\right)^3}=\dfrac{a^3+b^3}{c^3+d^3}\\ \Rightarrow\dfrac{a^3+b^3}{\left(a+b\right)^3}=\dfrac{c^3+d^3}{\left(c+d\right)^3}\)
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