a) Sửa đề CMR : \(\left(\frac{a+b+c}{b+c+d}\right)^3=\frac{a}{d}\)
\(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}=\frac{a+b+c}{b+c+d}\)
=> \(\left(\frac{a}{b}\right)^3=\left(\frac{b}{c}\right)^3=\left(\frac{c}{d}\right)^3=\left(\frac{a+b+c}{b+c+d}\right)^3\)
=> \(\left(\frac{a}{b}\right)^3=\left(\frac{a+b+c}{b+c+d}\right)^3\)
=> \(\frac{a}{b}.\frac{a}{b}.\frac{a}{b}=\left(\frac{a+b+c}{b+c+d}\right)^3\)
=> \(\frac{a}{b}.\frac{b}{c}.\frac{c}{d}=\left(\frac{a+b+c}{b+c+d}\right)^3\left(\text{vì }\frac{a}{b}=\frac{b}{c}=\frac{c}{d}\right)\)
=> \(\frac{a}{d}=\left(\frac{a+b+c}{b+c+d}\right)^3\left(\text{đpcm}\right)\)
b) |17x - 5| - |17x + 5| = 0
=> |17x - 5| = |17x + 5|
=> \(\orbr{\begin{cases}17x-5=17x+5\\17x-5=-17x-5\end{cases}}\Rightarrow\orbr{\begin{cases}0x=10\\34x=0\end{cases}}\Rightarrow\orbr{\begin{cases}x\in\varnothing\\x=0\end{cases}}\Rightarrow x=0\)
Vậy x = 0 là giá trị cần tìm
