\(\frac{3x+25}{144}=\frac{2y-169}{25}=\frac{z+144}{169}=\frac{3x+2y+z}{338}=\frac{169}{338}=\frac{1}{2}\)
\(\Rightarrow3x+25=\frac{1}{2}.144=72\)
\(\Leftrightarrow x=\frac{47}{3}\)
\(2y-169=\frac{1}{2}.25=\frac{25}{2}\)
\(\Leftrightarrow y=\frac{363}{4}\)
\(z+144=\frac{1}{2}.169=\frac{169}{2}\)
\(\Leftrightarrow z=\frac{-119}{2}\)
Áp dụng tính chất dãy tỉ số bằng nhau
\(\frac{3x+25}{144}=\frac{2y-169}{25}=\frac{z+144}{169}=\frac{\left(3x+2y+z\right)+\left(25-169+144\right)}{144+25+169}=\frac{169+25-169+144}{144+25+169}=\)
\(\frac{1}{2}\)
Ta có
\(\frac{3x+25}{144}=\frac{1}{2}\Rightarrow6x+50=144\Rightarrow6x=94\Rightarrow x=\frac{47}{3}\)
\(\frac{2y-169}{25}=\frac{1}{2}\Rightarrow4y-338=25\Rightarrow4y=363\Rightarrow y=\frac{363}{4}\)
\(\frac{z+144}{169}=\frac{1}{2}\Rightarrow2z+288=169\Rightarrow2z=-119\Rightarrow z=\frac{-119}{2}\)
