Question

cho x y z biết (x + y + 3) / z = ( y + z + 1) / x = (x + z + 2) / y = 1 / (x + y +z)

Answer 1

ta co x+y+3/z=y+z+1/x=x+z+2/y=1/x+y+z, theo tinh chat cua day ti so bang nhau ta co

x+y+3/z=y+z+1/x=x+z+2/y=1/x+y+z=(3+1+2)+2x+2y+2z/z+y+x=6+2(x+y+z)/x+y+z=8

suy ra 1/x+y+z=8 suy ra x+y+z=1/8(1)

ta co x+y+3/z=y+z+1/x=x+z+2/y=8

suy ra x+y+3/z+1=y+z+1/x=x+z+2/y+1

suy ra x+y+z+3/z=y+z+x+1=x+z+y+2/y=9(2)

the (1) vao (2) ta co

1/8+3/z=1/8+1/y=1/8+2/x

suy ra 25/8/z=9/8/y=17/8/x

suy ra z=25/8:8=25/64

y=9/8:8=9/64

x=17/8:8=17/64

nho nhe