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ferary96
@ferary96
July 2022
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найдите все целочисленные решения уравнения
[tex] x^{2} + 5y^{2} + 34z^{2}+2xy-10xz-22yz=0[/tex]
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IUV
Verified answer
Х^2+5*у^2+34*z^2+2*х*у-10*х*z-22*у*z=0
(х+у-5z)^2+4y^2+9z^2-12yz=0
(х+у-5z)^2+(2y-3z)^2=0
х+у-5z=0
2y-3z=0
z=2*k
y=3*k
x=5*2*k-3*k=7*k
ответ (х;у;z) = (7k; 3*k; 2*k)
k - целое
6 votes
Thanks 3
IUV
утверждаю что
(х+у-5z)^2+(2y-3z)^2=х^2+5*у^2+34*z^2+2*х*у-10*х*z-22*у*z
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Answers & Comments
Verified answer
Х^2+5*у^2+34*z^2+2*х*у-10*х*z-22*у*z=0(х+у-5z)^2+4y^2+9z^2-12yz=0
(х+у-5z)^2+(2y-3z)^2=0
х+у-5z=0
2y-3z=0
z=2*k
y=3*k
x=5*2*k-3*k=7*k
ответ (х;у;z) = (7k; 3*k; 2*k)
k - целое
(х+у-5z)^2+(2y-3z)^2=х^2+5*у^2+34*z^2+2*х*у-10*х*z-22*у*z