Tham khảo nhé!
>>https://olm.vn/hoi-dap/detail/80507618602.html
#)Giải :
Ta có : \(c\left(b+d\right)=2bd\Rightarrow bc+cd=2bd\Rightarrow\frac{bc+cd}{a+c}=\frac{2bd}{2b}=d\)
\(\Rightarrow bc+cd=ad+cd\Rightarrow bc=ad\Rightarrow\frac{a}{b}=\frac{c}{d}\)
\(\frac{a}{b}=\frac{c}{d}\Rightarrow\hept{\begin{cases}\left(\frac{a}{b}\right)^8=\left(\frac{c}{d}\right)^8=\left(\frac{a+c}{b+d}\right)^8=\frac{a^8}{b^8}\\\left(\frac{a}{b}\right)^8=\left(\frac{c}{d}\right)^8=\frac{a^8}{b^8}=\frac{c^8}{d^8}=\frac{a^8+c^8}{b^8+c^8}\end{cases}}\)
\(\Rightarrow\left(\frac{a+c}{b+d}\right)^8=\frac{a^8+b^8}{c^8+d^8}\left(đpcm\right)\)
#)Góp ý :
Giải thích chi tiết ở đoạn a/b = c/d :
\(\frac{a}{b}=\frac{c}{d}\Rightarrow\left(\frac{a}{b}\right)^8=\left(\frac{c}{d}\right)^8=\left(\frac{a+c}{b+d}\right)^8\Rightarrow\frac{a^8}{b^8}=\frac{c^8}{d^8}\Rightarrow a^8d^8=b^8c^8\Rightarrow\frac{a^8}{c^8}=\frac{b^8}{d^8}=\frac{a^8+b^8}{c^8+d^8}\)
=> đpcm
P/s : Chắc bỏ cái c/m kia đi, lấy cái này chi tiết, dễ hiểu hơn ^^
