if the system of equation x= cy+bz,y=az+cx,z=bx+ay has a non zero value and at least one of it is proper fraction. prove that abc>-1 and a^3+b^3+c^3

Given system is a homogenous equation in 3 variables, its det will be zero because it is given that it has non zero value tht means infinnite solutions, hence det of coefficient matrix is zero after that u will get req result.