Home
Class 12
MATHS
If a , b , c are distinct real numbers a...

If `a , b , c` are distinct real numbers and the system of equations `a x+a^2y+(a^3+1)z=0` `b x+b^2y+(b^3+1)z=0` `c x+c^2y+(c^3+1)=0` has a non-trivial solution, show that `a b c=-1`

Promotional Banner

Similar Questions

Explore conceptually related problems

If a,b,c are distinct real numbers and the system of equations ax+a^(2)y+(a^(3)+1)z=0bx+b^(2)y+(b^(3)+1)z=0cx+c^(2)y+(c^(3)+1)=0 has a non-trivial solution,show that abc=-1

If a , b , c are non-zero real numbers and if the system of equations (a-1)x=y+z , (b-1)y=z+x , (c-1)z=x+y has a non-trivial solution, then prove that a b+b c+c a=a b c

If a , b , c are non-zero real numbers and if the system of equations (a-1)x=y=z (b-1)y=z+x (c-1)z=x+y has a non-trivial solution, then prove that a b+b c+c a=a b c

If a ,b ,c are non -zero real numbers and if the system of equations (a-1) x=y+z,(b-1)y=z+x,(c-1) z=x+y has a non -trivial solution, then prove that ab+bc+ca =abc .

The system of equations ax + 4y + z = 0,bx + 3y + z = 0, cx + 2y + z = 0 has non-trivial solution if a, b, c are in

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 a, b and c are non - zero real numbers and if system of equations (a-1)x=y+z, (b-1)y=z+x and (c-1)z=x+y have a non - trivial solutin, then (3)/(2a)+(3)/(2b)+(3)/(2c) is equal to

If a, b and c are non - zero real numbers and if system of equations (a-1)x=y+z, (b-1)y=z+x and (c-1)z=x+y have a non - trivial solutin, then (3)/(2a)+(3)/(2b)+(3)/(2c) is equal to