a)2/3x=3/4y=4/5z và x+y+z=196 b)x/2=y/3=z/4 và x^2+y^2+z^2=29 c)x/3=y/2=z/-3 và x.y.z=240 d)x/5=y/4=z/2 và x^3-y^3+z^3=69

\(\begin{array}{l} \dfrac{2}{3}x = \dfrac{3}{4}y = \dfrac{4}{5}z\\ \Leftrightarrow \dfrac{{2x}}{3} = \dfrac{{3y}}{4} = \dfrac{{4z}}{5}\\ \Leftrightarrow \dfrac{{2x}}{{3.12}} = \dfrac{{3y}}{{4.12}} = \dfrac{{4z}}{{5.12}}\\ \Leftrightarrow \dfrac{x}{{18}} = \dfrac{y}{{16}} = \dfrac{z}{{15}} = \dfrac{{x + y + z}}{{49}} = \dfrac{{196}}{{49}} = 4\\ \Rightarrow x = 18.4 = 72\\ y = 16.4 = 64\\ z = 15.4 = 60\\ b)\,\dfrac{x}{2} = \dfrac{y}{3} = \dfrac{z}{4} \Rightarrow \dfrac{{{x^2}}}{4} = \dfrac{{{y^2}}}{9} = \dfrac{{{z^2}}}{{16}} = \dfrac{{{x^2} + {y^2} + {z^2}}}{{4 + 9 + 16}} = \dfrac{{29}}{{29}} = 1\\ \Rightarrow {x^2} = 4 \Rightarrow x = \pm 2\\ {y^2} = 9 \Rightarrow y = \pm 3\\ {z^2} = 16 \Rightarrow z = \pm 4 \end{array}\)

\(\begin{array}{l} \dfrac{2}{3}x = \dfrac{3}{4}y = \dfrac{4}{5}z\\ \Leftrightarrow \dfrac{{2x}}{3} = \dfrac{{3y}}{4} = \dfrac{{4z}}{5}\\ \Leftrightarrow \dfrac{{2x}}{{3.12}} = \dfrac{{3y}}{{4.12}} = \dfrac{{4z}}{{5.12}}\\ \Leftrightarrow \dfrac{x}{{18}} = \dfrac{y}{{16}} = \dfrac{z}{{15}} = \dfrac{{x + y + z}}{{49}} = \dfrac{{196}}{{49}} = 4\\ \Rightarrow x = 18.4 = 72\\ y = 16.4 = 64\\ z = 15.4 = 60\\ b)\,\dfrac{x}{2} = \dfrac{y}{3} = \dfrac{z}{4} \Rightarrow \dfrac{{{x^2}}}{4} = \dfrac{{{y^2}}}{9} = \dfrac{{{z^2}}}{{16}} = \dfrac{{{x^2} + {y^2} + {z^2}}}{{4 + 9 + 16}} = \dfrac{{29}}{{29}} = 1\\ \Rightarrow {x^2} = 4 \Rightarrow x = \pm 2\\ {y^2} = 9 \Rightarrow y = \pm 3\\ {z^2} = 16 \Rightarrow z = \pm 4 \end{array}\)