Let =45 ; , , R . If x( , 1,2)+y(1, , 2)+z(2,3, )=(0,0,0) for some x, y, z R , x y z 0 , then 6 +4 + is equal to _______

Step-by-step solution

aligned & =45, R & x ( , 1,2)+ y (1, , 2)+ z (2,3, )=(0,0,0) & x , y , z R , xyz 0 & x + y +2 z =0 & x + y +3 z =0 & 2 x +2 y + z =0 & xyz 0 non-trivial & | array lll & 1 & 2 1 & & 3 2 & 2 & array |=0 aligned aligned & ( -6)-1( -6)+2(2-2 )=0 & -6 - +6+4-4 =0 & 6 +4 + =55 aligned