tim x,y,z biet; x/z+y+1=y/x+z+1=x+y-2=x+y+z
a, tim x€Z biet (x-6) chia het cho (x-5)
b, tim x€Z, y€Z biet (x-1).(xy-5)=5
Tim x y z biet x/(y-z)=y/(x+z)=z/(y-x)=x-y+z
Tim x,y,z biet x-y+z=x/(y*z)=y/(z+x)=z/(y-x)
tim x y z biet x-1/2=y-2/3=z-3/4 biet x-2y+3z=14
\(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}=\frac{x-1-2\left(y-2\right)+3\left(z-3\right)}{2-2.3+3.4}=\frac{x-2y+3z-6}{8}=1\)
\(\Leftrightarrow\hept{\begin{cases}x-1=2\\y-2=3\\z-3=4\end{cases}}\Leftrightarrow\hept{\begin{cases}x=3\\y=5\\z=7\end{cases}}\)
tim x,y,z biet x-y=2011;y-z=-2011;z+x=2013
Đặt x - y = 2011 (1)
y-z=2012 (2)
z+x = 2013 (3)
Cộng (1), (2), (3) vế ta được :
2.x = 2012 => x = 1006
Từ (1) => y = -1005
Từ (3) => z= 1007
tim x,y,z biet x-y=2011,y-z=-2012,z+x=2013
1 tim MAX cua (x+z)(y+t) biet x^2+y^2+z^2+t^2=1
2 tim MAX cua (x+z)(y+t) biet x^2+y^2+2z^2+2t^2=1
tim x,y,z biet /x/+/y/+/z/=0
tim x,y,z biet x=4y=0.4(y+z) va x+y+z = 2800