Ta có: \(\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{d}=\dfrac{d}{a}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{d}=\dfrac{d}{a}=\dfrac{a+b+c+d}{a+b+c+d}=1\)
\(\Rightarrow\dfrac{a}{b}=1\Rightarrow a=b\)
\(\dfrac{b}{c}=1\Rightarrow b=c\)
\(\dfrac{c}{d}=1\Rightarrow c=d\)
\(\Rightarrow a=b=c=d\)
\(\Rightarrow a^{20}.b^{17}.c^{2017}=d^{20}.d^{17}.d^{2017}=d^{2054}\)
đpcm
Tham khảo nhé~