a: Đặt x/8=y/3=z/10=k
=>x=8k; y=3k; z=10k
\(xy+yz+xz=1206\)
\(\Leftrightarrow24k^2+80k^2+30k^2=1206\)
=>134k2=1206
=>k2=9
TH1: k=3
=>x=24; y=9; z=30
TH2: k=-3
=>x=-24; y=-9; z=-30
b: x/4=2y/5=5z/6
=>\(\dfrac{x}{40}=\dfrac{2y}{50}=\dfrac{5z}{60}\)
=>x/40=y/25=z/12
Đặt x/40=y/25=z/12=k
=>x=40k; y=25k; z=12k
Ta có: \(x^2-3y^2+2z^2=325\)
\(\Leftrightarrow1600k^2-1875k^2+288k^2=325\)
=>k2=25
TH1: k=5
=>x=200; y=125; z=60
TH2: k=-5
=>x=-200; y=-125; z=-60
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