Bună!
[tex]x^{2} +y^{2} +z^{2} =116\\x*\frac{1}{4} =y*\frac{1}{6} =z*\frac{1}{8} =k\\\frac{x}{4} =\frac{y}{6} =\frac{z}{8} =k\\=> x=4k\\=>y=6k\\=>z=8k\\(4k)^{2} +(6k)^{2} +(8k)^{2} =116\\16k^{2} +36k^{2} +64k^{2} =116\\116k^{2} =116\\k=1\\=> x=4k=4*1=4\\=> y=6k=6*1=6\\=> z=8k=8*1=8\\sau \\k=-1\\=> x=-4\\=>y=-6\\=> z=-8[/tex]
