x ∈ Z
x/y+z+t+2015 = y/x+z+t+2015 , y/x+z+t+2015 = z/x+y+t+2015 , z/x+y+t+2015 = t/x+y+z+2015 , t/x+y+z+2015 = 2015 /x+y+z+t*x+y/z+t+2015 + y+z/x+t+2015 + z+t/x+y+2015 + (t+2015) /x+y+z + 2015 +x /y+z+t
giai he phuong trinh
x+y+z=2016
(x*y/x*x+x*y+y*y)+(y*z/y*y+y*z+z*z)+(z*x/z*z+z*x+x*x)=1
B1: Cho x,y,z = 0. Tính Q= ( x-y/z + y-z/x + z-x/y) ( z/x-y + x/y-z + y/ z-x)
B2: Cho x√x + y√y + z√z = 3√xyz. Tính Q = ( 1+ x/y) ( 1+ y/z)( 1+z/x)
suppose that x( x + y + z ) = 2; y( x + y + z ) = 25; z( x + y + z ) = -2;
Dịch: Cho x(x+ y + z) = 2; y(x + y + z) = 25; z (x + y + z) = -2. Tìm x; y ;z ( x> 0)
x(x+y+z) + y(x+y+z) + z(x+y+z) = 2 + 25 - 2 = 25
=> ( x+ y+ z )(x+y+z) = 25
=> x + y+ z = 5 hoặc x + y +z = -5
(+) x + y +z = 5 => x.5 = 2 => x = 2/5
=> y.5=5 => y = 1
=> z.5 = -2 => z = -2/5
(+) x+ y+ z = -5 => -5x = 2 => x= -2/5 (loại x > 0)
Vậy x = 2/5 ; y = 1 ; z = -2/5
Chứng minh rằng:
(y-z)/(x-y)(x-z) + (z-x)/(y-z)(y-x) + (x-y)/(z-x)(z-y) = 2/(x-y) + 2/(y-z) + 2/(z-x)
Chứng minh rằng:
(y-z)/(x-y)(x-z) + (z-x)/(y-z)(y-x) + (x-y)/(z-x)(z-y) = 2/(x-y) + 2/(y-z) + 2/(z-x)
L8 đã học hằng đẳng thức chưa e nhỉ?
x/y+z+t = y/x+t+z = z/x+y+t = t/x+y+z . Tính P = x+y / z+t + y+z/t+x + z+t/x+y + t+x / y+z