Question

cho a/b=b/c=c/d=d/m chứng minh: a/m=(a+b+c+d/b+c+d+m)^4

Answer 1

Đặt\(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}=\frac{d}{m}=k\Rightarrow a=bk;b=ck;c=dk;d=mk\)

\(\Rightarrow a=mk^4;b=mk^3;c=mk^2;d=mk\)

\(\Rightarrow\frac{a}{m}=\frac{mk^4}{m}=k^4\)và   \(\left(\frac{a+b+c+d}{b+c+d+m}\right)^4=\left(\frac{mk^4+mk^3+mk^2+mk}{mk^3+mk^2+mk+m}\right)^4=^{\left(\frac{mk\left(k^3+k^2+k+1\right)}{m\left(k^3+k^2+k+1\right)}\right)^4}=k^4\)

\(\Rightarrow\frac{a}{m}=\left(\frac{a+b+c+d}{b+c+d+m}\right)^4\)(đpcm)