Toán Lớp 7: Tìm các số hữu tỉ x, y, z biết rằng:
x(x+y+z) = -5; y(x+y+z) = 9; z(x+y+z) = 5
Leave a reply
Register Now
Login
Lost Password
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Toán Lớp 7: Tìm các số hữu tỉ x, y, z biết rằng:
x(x+y+z) = -5; y(x+y+z) = 9; z(x+y+z) = 5
Comments ( 2 )
⇒ (x+y+z).(x+y+z) = 9.
⇒ (x+y+z)^2 = 9.
⇒ \(\left[ \begin{array}{l}(x+y+z)^2=3^2.\\(x+y+z)^2=(-3)^2.\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}x+y+z=3.\\x+y+z=-3.\end{array} \right.\)
$\text{TH1:}$ x+y+z = 3:
(+) y(x+y+z) = 9 ⇒ x.3 = 9 ⇒ x = 9 : 3 ⇒ y = 3.
(+) z(x+y+z) = 5 ⇒ z.3 = 5 ⇒ z = 5 : 3 = 5/3.
$\text{TH2:}$ x+y+z = -3:
(+) z(x+y+z) = 5 ⇒ z.(-3) = 5 ⇒ z = 5 : (-3) = (-5)/3.
$\text{Vậy}$ (x;y;z) = ((-5)/3; 3; 5/3) hoặc (x;y;z) = (5/3;-3;(-5)/3).