The number of solutions (x, y, z) to the system of equations x+2 y+4 z=9,4 y z+2 x z+x y=13, x y z=3 Such that at least two of x , y , z are integers is -

Step-by-step solution

array l x+2 y+4 z=9 2 x y+8 y z+4 x z=26 (x)(2 y)(4 z)=24 array Say roots of P ³-9 P ²+26 P -24=0 are x , 2 y and 4 z Here (P-2) (P²-7 P+12 )=0(P-2)(P-3)(P-4)=0 now 4 z =4 ; 2 y =2 ; x =3 then (3,1,1)x=2 ; 2 y=4 ; 4 z=3 then (2,2, 3 4 ) x =3 ; 2 y =4 ; 4 z =2 then (3,2, 1 2 ) x =2 ; 2 y =3 ; 4 z =4 then (2, 3 2 , 1 ) x =4 ; 2 y =2 ; 4 z =3 then (4,1, 3 4 ) Hence there are five solutions.