20 BOOK OF MATHEMATICAL PROBLEMS. 



104. If x(b-c) + y(c-a) + z(a-b) = Q, then will 



bz cy cx az ay bx 

 b c c a a b 



105. If a?, y, z, u be all finite and satisfy the equations 



x = by + cz + du, 

 y = ax + cz + du, 

 z = ax + by -f du, 



thenwai 



106. If =*-* 



bc x ca y 



x 3 - y* xy 



then will -y- = : 



a-b z 



y>-z* z*-x* 



and if a + ^ - = b + - , 



b-c c-a 



x* y* 

 then will each member of the equation be equal to c + ^ . 



yz zx 



x-- y -- 



107. If , = ** , and x. y be unequal, then will each 



1 - yz l-zx' 



member of this equation be equal to , to x + y +z, andto 



i-xy 



I 1 1 



-+ -+ -. 

 x y z 



108. Having given the equations 



alx -f bmy + cnz = aXx + bm'y + criz = ax 3 + by 9 + cz* = 0, 

 prove that 



x (mri - m'n) + y (rd f - n't) + z (Im - I'm) = 0, 



