Question

yz=15 xz=10 y2+z2=34 система уравнений пожалуйста помогите напишите решение

Answer 1

y = 15/z
x = 10/x
z = 15/y
z = 10/x

$( frac{15}{z} )^2 + z^{2} = 34$
$frac{225}{ z^{2} } + z^{2} = 34 | * z^{2}$
$225 + z^{4} - 34 z^{2} = 0$
$z^{4} - 34 z^{2} +225=0$
Замена:
$z^{2} = a$
$a^{2}-34a+225=0$
D = 1156 - 900 = 256
$a_{1} = frac{34+ sqrt{256} }{2} = frac{34+16}{2}=25$
$a_{2} = frac{34-16}{2}=9$
$a) z^{2} = 25$
$z_{1} = 5$
$y_{1} = 15/5=3$
$x_{1} =10/5=2$
$z_{2} = -5$
$y_{2} = -15/5=-3$
$x_{2} =-10/5=-2$
б) $z^{2} = 9$
$z_{3} = 3$
$y_{3} = 15/3=5$
$x_{3} =10/3=3 frac{1}{3}$
$z_{4} = -3$
$y_{4} = -15/3=-5$
$x_{4} =-10/3=-3 frac{1}{3}$