BOOK OF MATHEMATICAL PROBLEMS. 



113. Prove the following equalities, having given that 

 a 4- b + c = 0, 



o + y + c" q + b* + c* a 8 4- b*+ c 8 

 5 3 2 



32 



(a 3 4-6 8 4-c 8 ) 8 a 8 4-5 8 4-c g 



11 3 2 9 



114. If a + 6 + c + c? = 0, then will 



115. Having given the equations 



(y + z)* = kcfyz, (z + x) a = 4b s zx, (x + yf = c*xy ; 



I>rove that 



a a + b* + c*2abc = l. 



116. Having given 



y z z x x y 



- -- = a, --- -b, - = c; 

 z y x z y x 



prove that 



26V 4- 2c V + 2a 8 6 a - a 4 - 6 4 - c 4 4- a*b V = 0. 



117. Having given the equations 



7 + cz' - ax') y (cz + ax - by) z (ax f + by - cz) ' 

 prove that, if x, y, z be all finite, 



