ALGEBRA. 23 



118. If the quantities x, y, z be all unequal and satisf\ 

 equations 



yz zx xy 



lember of the equations = a* 1, and 

 1 1 1 



- + - x+ -. 



119. If 



a c a 



wi 



x fb' c' a\* y (c a' b'\* z (a! b' c\* A 



-(T + --- ) + %(-+ -- T ) + - ( + T--) = - 

 a \b c aj b\c a bj c\a b c/ 



VI. Inequalities. 



The symbols employed in the following questions ar< 

 >oed to denote real quantities. 



The fundamental proposition on which the solution generally 

 Is is o* + b* >2ab. 



g values of cc! n-essions involving an unknown 



quantity in the second degree only maybe found i'n.m tl..- 

 dition that a quadratic equation shall have real roots : e. g. " To 



lie greatest aii dues of _ - T." Assuming the 



expression =y, we obtain the quadra 



and if x be a real quantity K iliis e<|uati >n 



3y > -3y<l, or (2y-l)'- 

 shewing that y must lie between the values 



