a:b=b:c=c:a=>a/b=b/c=c/a=a+b+c/b+c+a=1

suy ra: a/b=1 suy ra: a=b

b/c=1 =>b=c

suy ra: a=b=c

suy ra: a^2.b^2.c^1930:b^1935=1.1.1:1=1

Vì a/b=b/c=c/a => a=b=c => a³b²c¹⁹³⁰=a³a²a¹⁹³⁰= a¹⁹³⁵.Vậy a³b²c¹⁹³⁰/a¹⁹³⁵=a¹⁹³⁵/a¹⁹³⁵=1

ADTCDTSBN ta có a+b+c/b+c+a=1

=>a/b=1=>a=b

b/c=1=>b=c

=>a=b=c

ta có M=b^3.b^2.b^1930/b^1935=1

theo tích chất dãy tỉ số bằng nhau ta có

\(\frac{a}{b}=\frac{b}{c}=\frac{c}{a}=\frac{a+b+c}{b+c+a}=1\Rightarrow a=b=c\)

ta có\(\frac{a^3.b^2.c^{1930}}{c^{1935}}=\frac{c^3.c^2.c^{1930}}{c^{1935}}=\frac{c^{1935}}{c^{1935}}=1\)

Giải:

Áp dụng tính chất dãy tỉ số bằng nhau ta có:

\(\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{a}=\dfrac{a+b+c}{a+b+c}=1\)

\(\left\{{}\begin{matrix}\dfrac{a}{b}=1\Rightarrow a=b\\\dfrac{b}{c}=1\Rightarrow b=c\\\dfrac{c}{a}=1\Rightarrow c=a\end{matrix}\right.\Rightarrow a=b=c\)

\(\dfrac{a^3b^2c^{1930}}{a^{1935}}=\dfrac{a^3a^2a^{1930}}{a^{1935}}=\dfrac{a^{1935}}{a^{1935}}=1\)

Vậy \(\dfrac{a^3b^2c^{1930}}{a^{1935}}=1\)