Given that the system of equations `x=cy+bz ,y=az+cx , z=bx +ay` has nonzero solutions and and at least one of the a,b,c is a proper fraction.
`a^(2)+b^(2)+c^(2)` is

Given that the system of equations x=cy+bz ,y=az+cx , z=bx +ay has nonzero solutions and and at least one of the a,b,c is a proper fraction. abc is

If the system of equations x=cy+bz, y=az+cx and z=bx+ay has non-trivial solution and at least one of a,b, c is a proper fraction, prove that a^(2)+b^(2)+c^(2) lt 3 and abc gt -1

If the system of linear equations x=cy+bz , y=az+cx , z=bx+ay has a non trivial solution show that a^2+b^2+c^2+2abc=1

The system of equations ax-y- z=a-1 ,x-ay-z=a-1,x-y-az=a-1 has no solution if a is:

The system of equations -2x+y+z=a x-2y+z=b x+y-2z=c has

If the system of equations bx + ay = c, cx + az = b, cy + bz = a has a unique solution, then

If the system of equations x=c y+b z y=a z+c x z=b x+a y has a non-trivial solution, show that a^2+b^2+c^2+2a b c=1

If the system of equations x=c y+b z ,\ \ y=a z+c x ,\ \ z=b x+a y has a non-trivial solution show that a^2+b^2+c^2+2a b c=1

If the system of linear equations x+2ay +az =0,x+3by+bz =0 and x+4cy + cz =0 has a non-zero solution, then a, b, c

If the system of linear equations x + 2ay + az = 0 x + 3by + bz = 0 x + 4cy + cz = 0 has a non-zero solution, then a, b, c