Question

[Dương Thanh Ngân]

tìm x y z biết

\(\dfrac{3}{x-1}=\dfrac{4}{y-2}=\dfrac{5}{z-3}\),xyz=192

Answer 1

[Nguyễn Lê Phước Thịnh]

\(\dfrac{3}{x-1}=\dfrac{4}{y-2}=\dfrac{5}{z-3}\)

\(\Leftrightarrow\dfrac{x-1}{3}=\dfrac{y-2}{4}=\dfrac{z-3}{5}=k\)

=>x-1=3k; y-2=4k; z-3=5k

=>x=3k+1;y=4k+3;z=5k+3

xyz=192

=>(3k+1)(4k+3)(5k+3)=192

=>(12k^2+13k+3)(5k+3)=192

=>60k^3+36k^2+65k^2+39k+15k+9=192

=>60k^3+101k^2+54k-183=0

=>k=0,92

=>x=3k+1=3,76; y=4k+3=6,68; z=7,6